Question

A colony of bacteria is increasing at the rate of 15% each hour. There are 3,500 bacteria in the colony at the time observations begin. Find an exponential growth model for A, the number of bacteria t hrs after the first observation.

Answer 1

Answer:

$A(t) = 3500e^{0.15t}$

Step-by-step explanation:

An exponential function for the colony of bacteria has the following format:

$A(t) = A(0)e^{rt}$

In which A(t) is the population after t hours, A(0) is the initial population and r is the growth rate.

There are 3,500 bacteria in the colony at the time observations begin.

This means that A(0) = 3500.

A colony of bacteria is increasing at the rate of 15% each hour.

This means that $r = 0.15$

Find an exponential growth model for A, the number of bacteria t hrs after the first observation.

$A(t) = A(0)e^{rt}$

$A(t) = 3500e^{0.15t}$