Question

homework assignment 6.1 exponential functions
due sunday by 11:59pm points 12 submitting an external tool
homework assignment 6.1 exponential functions
score: 0/12 answered: 0/12
question 1
a population numbers 14,000 organisms initially and decreases by 8.4% 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 = ab^t ), where
( p = )
question help: video 1 video 2 read 1 written example 1

Explanation:

Step1: Determine the initial value \(a\)

The initial population is \(14000\), so \(a = 14000\).

Step2: Determine the base \(b\)

The population decreases by \(8.4\%\) each year. The remaining percentage is \(100\% - 8.4\%=91.6\% = 0.916\), so \(b = 0.916\).

Step3: Write the exponential model

Substitute \(a = 14000\) and \(b = 0.916\) into \(P=ab^{t}\), we get \(P = 14000\times(0.916)^{t}\).

Answer:

\(P = 14000\times(0.916)^{t}\)