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 8.5 mm and an observed doubling time of 11 minutes.

(a) Lett be the time (in days) passed, and let y be the area of the sample at time t. Oino Write a formula relating y to 1. S Use exact expressions to fill in the missing parts of the formula. Do not use approximations. y =

Answer 1

The area of the bacteria population grows according to the formula y = 8.5(2^(t/(11/1440))), where y is the area in mm^2, t is the time in days, and the doubling time is converted from 11 minutes to days by dividing by 1440, which is the number of minutes in a day.

Step-by-step explanation:

To derive the formula relating the area covered by a bacteria population (y) to the time passed in days (t), we need to use the exponential growth model. Given the initial area of 8.5 mm2 and a doubling time of 11 minutes, we can use the general exponential growth formula:

y = a(2t/T)

Where:

• a is the initial amount (8.5 mm2)
• T is the doubling time in the same units as t (We must convert 11 minutes into days)
• t is the time in days
• Since there are 1440 minutes in a day, T in days will be 11/1440.

So we can rewrite the formula as:

y = 8.5(2t/(11/1440))