Question

a population numbers 16,000 organisms initially and grows by 7.5% each year. suppose p represents population, and t the number of years of growth. an exponential model for the population can be written in the form p = a·b^t where a = and b = . question help: message instructor

Explanation:

Step1: Determine the value of \(a\)

In the exponential growth model \(P = a\cdot b^{t}\), \(a\) represents the initial amount. The population initially has 16,000 organisms, so \(a = 16000\).

Step2: Determine the value of \(b\)

The population grows by 7.5% each year. To find the growth factor \(b\), we add the growth rate (expressed as a decimal) to 1. The growth rate of 7.5% is \(0.075\) in decimal form. So, \(b=1 + 0.075=1.075\).

Answer:

\(a = 16000\), \(b = 1.075\)