Question

A population of 20,000 is decreasing in size at a rate of 4.6% each year. Let A(t) representthe amount in the population after t years. (same as previous problem)Determine when the population will reach below 5000. Round to the nearest thousandth ofa year.

Answer 1

`\begin{gathered} A(t)=20000-(20000*4.6)/(100)t \\ A(t)=20000-920t \end{gathered}`

solve t when A(t)=5000

`\begin{gathered} 5000=20000-920t \\ 920t=20000-5000 \\ 920t=15000 \\ t=16.3 \end{gathered}`

the population will be below 5000 after 16.3 years