Chapter 6.4, Problem 36HP

To determine

To find: Predicted, actual population and percent error.

Answer to Problem 36HP

Predicted population = $1760$

Actual population $=1840$

Percent error $=-4.345\%$

Explanation of Solution

Given information:

Student population at present $=1600$ .

Student population predicted to rise $10\%$ in five years.

Actually, population rose $15\%$ .

Percent error $=\frac{A}{O}\times 100$

Where

  $A=$ Absolute value.

  $O=$ Actual value.

From given information

Student population at present $=1600$ .

Student population predicted to rise $10\%$ in five years.

Predicted value of population after five years = student population at present $+$ 10% of student population.

Therefore

Predicted value = $1600+\left(\frac{10}{100}\times 1600\right)$

  $\Rightarrow$ Predicted value = $1600+\left(0.1\times 1600\right)$

  $\Rightarrow$ Predicted value = $1600+160$

  $\Rightarrow$ Predicted value = $1760$

Student population at present $=1600$ , Actually, population rose $15\%$ .

Actual value of population after five years = student population at present $+$

  $15\%$ of student population.

Actual value = $1600+\left(\frac{15}{100}\times 1600\right)$

  $\Rightarrow$ Actual value = $1600+\left(0.15\times 1600\right)$

  $\Rightarrow$ Actual value = $1600+240$

  $\Rightarrow$ Actual value = $1840$

Absolute value = predicted value $-$ Actual value.

  $\begin{array}{l}\Rightarrow A=1760-1840\\ \Rightarrow A=-80\end{array}$

Therefore,

Percent error $=\frac{-80}{1840}\times 100$

  $\Rightarrow$ Percent error $=\frac{-8000}{1840}$

  $\Rightarrow$ Percent error $=-4.345$

Therefore

Predicted population = $1760$

Actual population $=1840$

Percent error $=-4.345\%$