Question

A colony of bacteria is increasing at the rate of 15% each hour. There are 4,500 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

The exponential growth model for the number of bacteria t hours after the observation begins is A = 4500(1 + 0.15)^t, where A is the number of bacteria, starting with 4,500 and increasing by 15% each hour.

Step-by-step explanation:

The student has asked for an exponential growth model of a bacterial colony that increases at a rate of 15% each hour, starting with 4,500 bacteria. To find the model A representing the number of bacteria t hours after the first observation, we can use the formula for exponential growth: A = P(1 + r)^t, where P is the initial amount, r is the growth rate, and t is time in hours.

The initial amount P is 4,500 bacteria, and the growth rate r is 15%, which is 0.15 in decimal form. Thus, the exponential growth model is A = 4500(1 + 0.15)^t.

If we want to clarify using a numerical example, after one hour, t would be 1, and the model would predict: A = 4500(1 + 0.15)^1 = 4500 * 1.15 = 5175 bacteria.