Question

a population numbers 18,000 organisms initially and grows by 6.2% 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 p =

Explanation:

Step1: Identify the initial value (a)

The initial population is 18,000, so \( a = 18000 \).

Step2: Determine the growth factor (b)

The population grows by 6.2% each year. To find \( b \), we add the growth rate (converted to a decimal) to 1. So \( b = 1 + 0.062 = 1.062 \).

Step3: Write the exponential model

Substitute \( a = 18000 \) and \( b = 1.062 \) into the formula \( P = a \cdot b^t \). So \( P = 18000 \cdot (1.062)^t \).

Answer:

\( P = 18000 \cdot (1.062)^t \)