Question 14
Yse the techniques of College Algebra to demonstrate your answer to the following.
A population numbers 11,000 organisms initially and grows by $15.3 \%$ 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 $P=a \cdot b^{t}$ where
\[
a=
\]
and $b=$
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Final Answer: \(a = 11000\) and \(b = 1.153\)
Step 1 ：The question is asking for the values of 'a' and 'b' in the exponential growth model. In this case, 'a' represents the initial population and 'b' represents the growth rate.
Step 2 ：The initial population is given as 11,000 organisms. Therefore, 'a' is 11,000.
Step 3 ：The growth rate is given as 15.3% per year. In the exponential growth model, this needs to be expressed as a decimal. Therefore, 'b' is 1 + 0.153 = 1.153.
Step 4 ：Final Answer: \(a = 11000\) and \(b = 1.153\)
