Acolony of bacteria grows according to the uninhibited growth model. suppose there is 18 g of bacteria on monday and 54 g of bacteria on wednesday. (a) find a function that gives the amount of bacteria in grams after t days. (use the variable a to represent the initial amount.) a(t) = (b) what is the doubling time for the colony? (round your answer to 2 decimal places.)

a. The general form of equation of an uninhibited growth model is:

A = a e^kt

where A is final amount, a is initial amount, k is constant and t is time

From Monday to Wednesday, two days have passed so t = 2, therefore calculating for constant k:

54 = 18 e^k(2)

e^2k = 3

2k = ln 3

k = 0.55

So the function becomes:

A(t) = a e^0.55t

b. Finding for t when A = 2a

2a = a e^0.55 t

0.55 t = ln 2

t = 1.26 days

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

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step-by-step explanation: