Question

May I just get the answer I don’t need elaboration

Answer 1

An exponential decay model is given in the form:

`y=a(1-r)^x`

where a is the initial population and r is the decay rate in fraction.

From the question, we have the following parameters:

`\begin{gathered} a=100 \\ r=4.5\%=0.045 \end{gathered}`

Therefore, the exponential model is given to be:

`y=100(1-0.045)^x`

From the options provided, there might be no need to solve any further to get the time when the population will be less than 50. However, we can solve it as shown below:

`\begin{gathered} 50=100(1-0.045)^x \\ (50)/(100)=0.955^x \\ Solving \\ x=15.05 \end{gathered}`

This means that it would take greater than 15 years for the population to get less than 50, approximately 16 years.

The correct option is the SECOND OPTION.