Chapter 4.1, Problem 1E

Solution

To Find: The initial amount, the growth factor, and the percent increase of the exponential growth model is $y=2.4{\left(1.5\right)}^x$ .

The initial amount is $\left(2.4\right)$ .

The Percent increase is $\left(0.5\right)$ .

The Growth factor is $\left(1+r\right)=1.5$ .

Given:

Expression: $y=2.4{\left(1.5\right)}^x$

Concept Used:

When a real-life quantity increases by a fixed percent each year or other time period, the amount y of the quantity after t year can be modeled by the equation $y=a{\left(1+r\right)}^t$ .

Where a is the initial amount and r is the percent increase expressed as a decimal, the quantity is the growth factor.

Calculation: exponential growth model expression is .

  $y=a{\left(1+r\right)}^t$

  $y=2.4{\left(1.5\right)}^x$

On comparing the above two equation:

  $\begin{array}{c}a=2.4\\ 1+r=1.5\\ r=1.5-1\\ r=0.5\end{array}$

The initial amount is $\left(2.4\right)$ .

The Percent increase is $\left(0.5\right)$ .

The Growth factor is $\left(1+r\right)=1.5$ .