Question

there are 20, 000 owls in the wild. Every year the owl population decrease 8%.identify the state. the starting amount the rate change this growth or decay justify .write the equation that represents the owl population after a number of years. how many owls will there be after six years

Answer 1

Given:

Number of owls in the wils is 20,000.

The rate of decrease is 8%.

From the given data the starting amount of owls is 20000.

The rate of change is -8%.

The general exponential equation of population growth is,

`P=P_0(1+(r)/(100))^t`

Here t represents the number of years.

Substitute the given values in the above equation,

`\begin{gathered} P=20000(1+(-(8)/(100)))^t \\ P=20000(1+(-0.08))^t \\ P=20000(1-0.08)^t \\ P=20000(0.92)^t \end{gathered}`

Hence, the required equation that represents the owl population after a number of years is obtained.

The number of owls after 6 years can be calculated by substituting t = 6 in the above equation.

`\begin{gathered} P=20000(0.92)^6 \\ P=20000(0.606355) \\ P=12127 \end{gathered}`

Hence, the population of owls in the wild is 12,127 after 6 years. And the population is decreasing.