Answer:
3125 bacteria.
Step-by-step explanation:
We can write an exponential function to represent the situation.
We know that the current population is 100,000.
The population doubles each day.
The standard exponential function is given by:
[tex]P(t)=a(r)^t[/tex]
Since our current population is 100,000, a = 100000.
Since our rate is doubling, r = 2.
So:
[tex]P(t)=100000(2)^t[/tex]
We want to find the population five days ago.
So, we can say that t = -5. The negative represent the number of days that has passed.
Therefore:
[tex]\displaystyle P(-5)=100000(2)^{-5} = 100000 \Big( \frac{1}{32}\Big) = 3125 \text{ bacteria}[/tex]
However, we dealing within this context, we really can't have negative days. Although it works in this case, it can cause some confusion. So, let's write a function based on the original population.
We know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, our function is:
[tex]P(t)=A(2)^t[/tex]
After 5 days, we reach the 100,000 population. So, when t = 5, P(t) = 100000:
[tex]100000=A(2)^5[/tex]
And solving for A, we acquire:
[tex]\displaystyle A=\frac{100000}{2^5}=3125[/tex]
So, our function in terms of the original day is:
[tex]P (t) = 3125 (2)^t[/tex]
So, it becomes apparent that the initial population (or the population 5 days ago) is 3125 bacteria.
Answer:
We can express the question in a exponential function
The current population is 100,000.
The population doubles each day.
The exponential function is given by: P(t)=a(r)^t
The current population is 100,000, a = 100000.
The rate is doubling, r = 2.
P(t)=100000(2)^t
As we know that the bacterial population had been doubling for 5 days. Let A represent the initial population. So, the function is:
P(t)=A(2)^t
After 5 days, the population reaches 100,000. So, when t = 5, P(t) = 100000:
100000=A(2)⁵
Now solving for A, we get
A=(100000)/(2⁵)=3125
So, the function in terms of the original day is:
P (t) = 3125 (2)^t
Hence, the initial population is 3125 bacteria.
3125 is the right answer.The price of a laptop changed from $350.00 to $550.00. What is the percent change in the cost of the laptop? 200% increase 200% decrease 57.14% increase 57.14% decrease
Answer:
57.14% increase
Step-by-step explanation:
$350÷$200(amount of increase) = 0.5714
0.5714×100= 57.14%
What is the value of the exponential expression5^0
An angle measures 10° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
50º & 40º
Step-by-step explanation:
complementary anlges add up to 90º. so, we can make an equation:
x+x-10=90
2x=100
x=50
so the angles are 50º and 40º.
A dog kennel board dogs for $8 a day. The kennel will also groom a dog for $12. Write an equation that gives the total cost of lodging a dog and having it groomed once before it comes home.
Andrew has $800 saved in his bank account, and he adds $50/month from his
allowance.
Answer:
So if you want an equation its
800+50x=?
So x could be the amount of months
Solve for m. 4 = 20m Simplify your answer as much as possible.
Answer:
0.2
Step-by-step explanation:
Which property is illustrated by the following?
a + 4 = a + 4
Answer: communitive
Step-by-step explanation:
The opposite sides have the same equations
Answer:
4
Step-by-step explanation:
If f(x) = 5 + 4(x - 4)?,
what is f(7)?
Answer:
Let's solve for f.
x=5+4(x−4)f(7)
Step 1: Flip the equation.
28fx−112f+5=x
Step 2: Add -5 to both sides.
28fx−112f+5+−5=x+−5
28fx−112f=x−5
Step 3: Factor out variable f.
f(28x−112)=x−5
Step 4: Divide both sides by 28x-112.
f(28x−112)28x−112=x−528x−112
f=x−528x−112
Answer:
f=x−528x−112
Are these triangles similar?
Answer:
Not similar, one has 4 sides
Step-by-step explanation:
I need help with this
Answer:
C
Step-by-step explanation:
You have to distribute the negative into the second set of parentheses first, and since 2x is positive, it will be negative, -3 is negative so it will be positive, and 18 is positive so it will be negative
Which expression is equivalent to 1/3y?
1. 1/3 (y + 12) - 12
2. 1/6y+ 1/3 (y+3)
3.1/6y+ 1/6(y+12)-2
4. 1/3y +1/3(6-y)
Please hurry I’m in a meet :,(
Step-by-step explanation:
1/6y+ 1/6(y+12)-2
hope it helps !
CAN SOMEONE PLEASE HELP ME SOLVE THIS
x^6+3x^3-5
write the expression in quadratic form
Step-by-step explanation:
[tex]v = {x}^{3} \\ {v}^{2} + 3v - 5 = 0 \\ [/tex]
Solving this equation using the quadratic formula, we get two real solutions :
1.1926 or -4.1926
Now we know the values of v , we can calculate x since x is ∛ v
[tex] {x}^{6} + 3 {x}^{3} - 5 = 0[/tex]
[tex]x = \sqrt[3]{1.1926} = 1.0605 \\ x = \sqrt[3]{ - 4.1926} = - 1.6125[/tex]
Kathy is going to buy a book at the bookstore for $9.45. The tax rate is 10%. What is the total cost Kathy would have to pay?
Can someone answer these two questions I submitted a photo of them it’s worth 50 points
Answer:
Step-by-step explanation:
1). Let the equation of the line is,
y = mx + b
Here, m = slope of the line
b = y-intercept
Slope of a line passing through two points,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We take two points from the table given (-3, -19) and (0, -1)
m = [tex]\frac{-19+1}{-3-0}[/tex]
m = 6
y - intercept 'b' = -1 [For x = 0]
Therefore, equation of the line will be,
y = 6x - 1
2). Equation of a line passing through a point (x', y') is,
y - y' = m(x - x')
Slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We take two points from the given table as (2, 12) and (3, 18).
Slope of the line passing through these points will be
m = [tex]\frac{18-12}{3-2}[/tex] = 6
Equation of the line passing through (2, 12) will be,
y - 12 = 6(x - 2)
y = 6x - 12 + 12
y = 6x
By using a graphing tool we can graph these lines representing the tables.
A cell phone normally sells for $500, but it is marked down 30% and you have a coupon for an additional 15% off. How much would it cost you to purchase the cell phone?
Answer:
$275
Step-by-step explanation:
30% + 15%=45%
45% of 500 is 225, because 500 x 0.45=225. Then subtract the discount from the total, 500 - 225, and you get 275
What is 3 [2^3+ (4-2)^3 - (6-2)^2] simplified
Answer:
Step-by-step explanation:
.. 3 + 2[4(2) – (4 + 3(2))]. 3 + 2[8 – (4 + 6)]. 3 + 2[8 – (10)]. 3 + 2[–2]. 3 – 4. –1 ... 2x + 6 = 4 – 2 + 1x. 2x + 6 = 2 + x. 2x – x + 6 = 2 + x – x. x + 6 = 2. x + 6 – 6 = 2 – 6. x = –4.
Find the value of x.
A. 5 root 2/2
B. 5
C. 10
D. 10 root l2
Simplify. 32 + 1 x 2 (1).8 (2).20 (3).14 (4).11
Answer:
31.11
Step-by-step explanation:
simplify the expression
Which graph shows that Cindy reads 3/4 of the time while riding in the car
Answer:
to solve this we would need to see the graphs
Step-by-step explanation:
however whichever one has 4 parts and 3 of them would be the time she spends reading.
2x+y=17 in slope intercept form
Answer:
y=-2x+17
Step-by-step explanation:
So the problem is 2x+y=17, we know that slope intercept form is y=mx+b where m is the slope and b is the y-int.
All you have to do is isolate the y.
2x+y=17
-2x on both sides so you can leave the y alone.
y=-2x+17 should be the answer. Hope this helps!
PLEASE HURRY THIS IS TIMED
Answer:
Plot a point on (0,1). Then count upwards by 9, and over to the right by 1. Then you're done!
Step-by-step explanation:
Hope this helps! <3
A student says that the equation y = 4x + 2 can be written in standard form as 4x − y = 2. Is the student correct?
Answer: I think so
Step-by-step explanation:
y=x+3
y=x-3
Solve these equations
Answer:
what is x?
Step-by-step explanation:
Answer:
No solutions
Step-by-step explanation:
please help! everything is in the ss below
Answer: A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
c - 12 > -16
+ 12 + 12
c > -4
Which of the following could be the measure of a pair of consecutive angles in a parallelogram?
Select the best answer from the choices provided.
A.
120° and 80°
B.
140° and 40°
C.
30° and 60°
D.
156° and 34°
Answer:b
Step-by-step explanation:it equals out to 180°
Franz used 1/12
of his new shelf space for novels and 1/3
for textbooks.
i) What fraction of his shelf space did he use?
ii) What fraction of shelf space is left for his other books?
Answer:
1/12+1/3=5/12
1-5/12=7/12
Step-by-step explanation:
add fractions used
remaining space ,subtract used fraction from the total
On that day the bakery gave away a total of 29 free gingerbread man cookies what was the total number of free candy canes the bakery gave away on that day show how or explore how you got your answer
Answer: 19 people
Step-by-step explanation:
If every 4th customer received a free gingerbread man cookie and 29 cookies were given away then the number of customers that came were:
= 4 * 29
= 116 customers
Because 116 customers came, they were able to give 29 cookies by giving one to every 4th customer.
If there were 116 customers, the number of customers who got the free candy canes would be:
= 116/6
= 19.3
= 19 people
Solve the system of equations below by elimination.
(Show your work)
x+2y=−4
x+y=2
please answer?!!!?!?