Question

A population numbers 14,000 organisms initially and grows by 11% 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 twhere

Answer 1

The exponential model for the population is P = 14,000 * (1.11)^t.

Step-by-step explanation:

The subject of this question is Mathematics and it is at a High School level.

To find the exponential model for the population, we need to determine the values of 'a' and 'b'.

Since the population grows by 11% each year, the growth factor 'b' can be calculated as (100% + 11%) = 111% = 1.11.

Using the initial population of 14,000, we can substitute the values into the exponential model P = a * b^t. We get 14,000 = a * (1.11)^0, which simplifies to 14,000 = a * 1. Solving for 'a', we find a = 14,000.

Therefore, the exponential model for the population is P = 14,000 * (1.11)^t.

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