A biologist observed a population of bacteria that grew at a rate expressed by the exponential equation
f(t) = 256e0.06111)
where t is in minutes. How long will it take the population to reach 5 times its initial value?
Round to two decimal places and do not include "t =" in your answer.
Answer:
It will take 26.34 minutes for the population to reach 5 times its initial value
Step-by-step explanation:
Exponential Growing
The population of bacteria grows at a rate expressed by the equation:
[tex]f(t)=256e^{0.06111t}[/tex]
Where t is in minutes.
We need to know when the population will reach 5 times its initial value. The initial value can be determined by setting t=0:
[tex]f(0)=256e^{0.06111\cdot 0}=256\cdot 1=256[/tex]
Now we find the time when the population is 5*256=1,280. The equation to solve is:
[tex]1,280=256e^{0.06111t}[/tex]
Dividing by 256:
[tex]e^{0.06111t}=1,280/256=5[/tex]
Taking natural logarithms:
[tex]ln\left(e^{0.06111t}\right)=ln5[/tex]
Applying the logarithm properties:
[tex]0.06111t=ln5[/tex]
Solving for t:
[tex]t=ln5/0.06111=26.34[/tex]
It will take 26.34 minutes for the population to reach 5 times its initial value
Your friend says the absolute value equation |3x+8|-9=-5 has no solution because the constant on the right side of the equation is negative. Is your friend correct?
Make sure to show the work and solution the problem, as well as the explanation.
Answer:
No, ur friend is not correct
| 3x + 8 | - 9 = -5 You have to get the absolute value (and everything in it) on one side of the equal sign, and everything else on the other side. So we have to get that -9 across the equal sign by adding 9 to both sides.
| 3x + 8 } = -5 + 9
| 3x + 8 | = 4 So that number is not negative anymore.
now u can set up ur 2 equations and solve for x, your 2 equations would be:
3x + 8 = 4 and 3x + 8 = -4
** If that -9 would not have been there, then ur friend would have been correct.
Hope this helps!!
Step-by-step explanation:
Your $960 got an interest rate of 8.7% which was
compounded monthly for 3 years. What is your $960
worth after 3 years?
Answer:
D
Step-by-step explanation:
Mitchell’s dog is 1/3 the age of Kayla’s cat . The sum of their ages is 12 years. How old is Mitchell’s dog?
Answer:
Mithcells dog is 3
Step-by-step explanation:
if its one third then you divide by 4 and get 3.
checking your answer
if mitchells dog is 3 and kaylas cat is three times that it would be 9
9+3=12
sorry if this is wrong :)
can you help me please
Answer: D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
What is the value of n?
| n | = 5
Answer:
5
Step-by-step explanation:
Answer:
Step-by-step explanation:
When you think you know what n is, check your answer. Add n to 7 and divide by 4. Do you get 5?
Given Triangle DEF has point D(-1,-5), E(-2,-1) and F(-4,-3) and is
rotated around the origin 90 degrees clockwise onto triangle D'E'F, what
are the coordinates of D'. E', and F?
Answer:
i think its f
Step-by-step explanation:
In 1998, the population of country C was 38 million, and the exponential growth rate was 1% per year
Answer:
Step-by-step explanation:
Formula for the exponential graph is given by the function,
[tex]P(t) = P_0(1 + r)^t[/tex]
Where [tex]P(t)[/tex] = population after 't' years
[tex]P_0[/tex] = Initial population
r = rate of increase
t = Number of years
In 1988, population of a country C was 30 million.
A). Function for the population will be,
[tex]P(t)=38(1+0.01)^t[/tex]
[tex]=38(1.01)^t[/tex]
B). Population in year 2020,
[tex]P(22)=38(1.01)^{22}[/tex]
= 47.30 million
C). Doubling time means the duration in which [tex]P_0[/tex] becomes [tex]2(P_0)[/tex].
[tex]P(t)=2P_0[/tex]
[tex]2P_0=P_0(1.01)^t[/tex]
[tex](1.01)^t=2[/tex]
By taking log on both the sides of the equation,
t[log(1.01)] = log2
t = [tex]\frac{\text{log}(2)}{\text{log}(1.01)}[/tex]
= [tex]\frac{0.30103}{0.004321}[/tex]
t = 69.66 years
WILL GIVE FREE BRIANLY IF U ANSWER whats 546.1 × 0.52
Answer: 283.972 is ur answer
Answer:
283.972
Step-by-step explanation:
now thats big brain
Simplify the expression.
(2x + 1/2) + (7x - 6 1/2)
Answer:
9x
Step-by-step explanation:
1 The graph below represents a jogger's speed during her 20-minute jog around her neighbor.
Answer:
4) She was jogging at a constant rate.
Step-by-step explanation:
In any graph that has to do with time and speed, anytime the line plateaus (flattens out), that means speed is at a constant rate.
what is the radius of a sphere with the volume of 12348pi
Answer:lemme see
Step-by-step explanation:
What is the leading coefficient of the following polynomial?
5x2-3x+6
Answer:
The 3
Step-by-step explanation:
Only correct answers get brainliest.
Answer:
x=3+ln(6)ln(4)
Step-by-step explanation:
if it takes seyi twenty minutes to boil an egg, how long will it take ala who is three years older than seyi to boil four eggs?
same twenty minutes
Answer:
time is constant
dolphin jet ski shop charges a flat fee of $37.00 plus $1.25 per hour to rent a jet ski. Marlin Jet Ski charges a fee of $30.00 plus $3.00 per hour to rent the same jet ski. Find the number of hours for which the costs are the same
Answer:
4 Hours, is when they will be the same.
Step-by-step explanation:
1.25 x 4 = 5.00 + 37.00 = 42.00
3.00 x 4 = 12.00 + 30.00 = 42.00
Therfore, at 4 hours they will be the same.
(yay)
Habib and Ali are friends and basketball coaches too. Habib goes to school every 4 days and Ali goes every 6 day to coach the students . if they both had a coaching session today. how many day in the next 48 days, would they both take the session on the same day? brainliest to the guy who send with the explanation
Answer:
I didn't got the ans but u can ask it to google assistant she is smarter than me
PLEASE HELP ME I WILL GIVE BRAINLEIST ASAP
The graph of f(x) is shown. What is the value of x when f(x) = 4?
Answer:
5
Step-by-step explanation:
The function intersects the y-axis at 1, and its slope is 1, so the function of the graph is y = x+1. Plugin 4, and you get y = 5.
5x - 10 = 4 + 6
Оа
10x - 20 = 10
Oь
5x - 10 = 10
Ос
X - 10 = 6
Od
3(5x - 10) = 30
5x = 0
5x = 20
Answer:
1.x=4
2.x=3
3.x=4
4.x=16
5.x=4
6.x=0
7.x=4
Answer:
1. x=4
2. x=3
3. x=4
4. x=16
5. x=4
6. x=0
7. x=3.9
Step-by-step explanation:
factor each completely
x²+x-30
A) (x+6)(x + 5)
B) (x – 6)(x – 5)
C) (x + 6)(x – 5)
D) (x + 1)(x + 5)
please
Terry is trying to place a satellite dish on the roof of his house at the recommended height of 18 feet. His house is 32 feet wide, and the height of the roof can be described by the function below,where x is the distance along the width of the house. Where should Terry place the dish? h(x) = -3/2 | x - 16 | + 24 A: No place is high enough B: Right at top C: 12 or 20 feet from the edge D: 4 or 28 feet from the edge
Answer:
C: 12 or 20 feet from the edge
Step-by-step explanation:
We are told the recommended height is 18 feet and that the function describing the height is;
h(x) = -(3/2)|x - 16| + 24
This means that;
-(3/2)|x - 16| + 24 = 18
Multiply through by -2/3 to give;
|x - 16| + 24(-2/3) = 18(-2/3)
|x - 16| - 16 = -12
Add 16 to both sides to get;
|x - 16| = 16 - 12
|x - 16| = 4
Add 16 to both sides to get;
Expanding the absolute value problem, we have;
x - 16 = 4 or -(x - 16) = 4
Thus;
x = 16 + 4 or -x + 16 = 4
x = 20 or x = 16 - 4
x = 20 or x = 12
Since x is the distance along the width of the house, then Terry should place the dish 12 or 20 feet from the edge
how do you write 4 copies of 3 tenths
Answer:
The answer is 1.2 hahahahahahahah very funny if you got it right.
Step-by-step explanation:
For how many different pairs of positive integers (a,b) with greatest common factor 1, and with a>b, does ab=30!
Answer:
4 pairs
Step-by-step explanation:
Given
ab = 30
Where
a > b
Required
Determine number of pairs (a,b)
To do this, we simply test values for a and b that satisfy the required condition.
First,
Take a = 30
Substitute 30 for a in ab = 30
30 * b = 30
b = 30/30
b = 1
The pair is (30,1)
Take a = 15
Substitute 15 for a in ab = 30
15 * b = 30
b = 30/15
b = 2
The pair is (15,2)
Take a = 10
Substitute 10 for a in ab = 30
10 * b = 30
b = 30/10
b = 3
The pair is (10,3)
Take a = 6
Substitute 6 for a in ab = 30
6 * b = 30
b = 30/6
b = 5
The pair is (6,5)
There exist no other pair that satisfy the given condition.
Counting the above pairs, there are just 4 pairs.
DISTANCES OF PLANETS TO SUN & EARTH Saturn Closest to sun: 135 billion km Mercury Closest to sun: 40 million km Closest to Earth: 773 million km Venus Closest to sun 107 million to Closest to Earth: 40 million km Earth Closest to sun: 147 million km Clowest to Earth:12 billion km Uranus Closest to sun 275 billion km Closest to Earth: 257 billion, kun Neptune Closest to sum: 4.45 billion km Closest to Earth: 43 billion km Pluto Mere Closest to sun 205 milion km Closest to Earth:05 million km Jupiter Closest to sun 41 million km Closest to sun 444 billion kan to Earth: 4.28 billion kin Closest to Earth 588 million km
Answer:
whats the question
Step-by-step explanation:
The numbers of copies of a college textbook sold quarterly over the past four years are: Since the time series has trend and seasonal pattern, to forecast the quarterly sales of the textbook, the following regression equation was found: stack y t with overparenthesis on top equals 2120 space minus 620 space Q t r 1 space minus space 1320 space Q t r 2 space plus space 290 space Q t r 3 space plus space 24 space t , where Q t r 1 , Q t r 2and Q t r 3 are dummy variables corresponding to Quarters 1, 2 and 3, and t = time period. The sales forecast for Quarter 3 of the next year is
Answer:
The predicted sales for the 4th quarter next year are 2168
Step-by-step explanation:
We formulate the given equation
Yt= 2120 - 620 Qtr 1 t -1320 Qtr 2 t + 290 Q tr3 t + 24 t
Taking the quarter 1 , 2 and 3 to be dummy variable the predicted sales for the 4th qtr are
Now put the values for the corresponding time period as 1,2 and 3
Yt= 2120 - 620 Qtr 1(0) -1320 Qtr 2(0) + 290 Q tr3 (0) + 24 (1)
Y(1)= 2120 + 24 = 2144 ( for year =1)
Y(2)= 2120+ 48= 2168 ( for year =2)
Y(3)= 2120 + 72= 2192 ( for year =3)
where t is the number of years.
So for the next year the fourth quarter sales are predicted to be 2168.
The sales forecast for Quarter 3 of the next year is 2192.
What is a sales forecast?It should be noted that a sales forecast simply means an expression for the expected sales revenue.
In this case, the sales forecast for Quarter 3 of the next year will be calculated thus:
= 2120 + 24(3)
= 2120 + 72
= 2192
Therefore, sales forecast for Quarter 3 of the next year is 2192.
Learn more about sales forecast on:
https://brainly.com/question/1101125
63-(-4) subtracting integers
Answer:
67
Step-by-step explanation:
the negative 4 cancels out with subracting turning it into an addition problem
Hello.
We are subtracting a negative number.
When we subtract a negative number, it cancels itself out, and it becomes an addition problem.
63-(-4) becomes 63+4
63+4 = 67
67 is the final answer.
How can insurance protect you from financial loss?
Insurance can offer easy monthly payment options for premiums.
Insurance can offer warranties on household items.
Insurance can offer low co-insurance policies.
Insurance can cover you or your property in case of an accident, theft, or another unpredictable event.
Answer:
Insurance can cover you or your property in case of an accident, theft, or another unpredictable event.
5. Write the following as a decimal: Forty-three thousandths
0.043
0.43
43,000
0.0043
Answer:
The answer would be A)
Step-by-step explanation:
Please help ASAP! I’ll mark you brainly
2. Light is captured using__________
the absorbed light is passed along
throughout molecules
and pigments until it is transferred to a single__________.
Step-by-step explanation:
Chloroplasts (left) convert light energy into chemical energy. High-energy electrons in chloroplasts are transported through two photosystems (right). ... The energy of light captured by pigment molecules, called chlorophylls, in chloroplasts is used to generate high-energy electrons with great reducing potential.
I hope this helps
Len wants to write the number 100,000 using a base of 10 and a exponent. What number should he use as the exponent.
Answer:
5
Step-by-step explanation:
5 would be your exponent because you count the number of zeros in the number and that is how many times you time 10 by 10
