The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of 1.3mm^(2) and an observed doubling time of 23 minutes. (a) Let t be the time (in minutes) passed, and let y be the area of the sample at time t. Write a formula relating y to t. Use

Question

The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of

1.3mm^(2)

and an observed doubling time of 23 minutes. (a) Let

t

be the time (in minutes) passed, and let

y

be the area of the sample at time

t

. Write a formula relating

y

to

t

. Use exact expressions to fill in the missing parts of the formula. Do not use approximations.

y=◻e^((◻)t)

(b) What will the area of the sample be in 8 minutes? Do not round any intermediate computations, and round your answer to the nearest tenth.

mm^(2)

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