Question

question 10 (multiple choice worth 2 points) (exploring exponential functions lc) what is the percent rate of change in the function $f(x) = 100 \cdot 1.7^x$? the percent rate of change shows 70% growth. the percent rate of change shows 17% growth. the percent rate of change shows 30% growth. the percent rate of change shows 170% growth.

Explanation:

Step1: Recall the exponential function form

The general form of an exponential growth function is \( f(x) = a(1 + r)^x \), where \( a \) is the initial amount, \( r \) is the growth rate (as a decimal), and \( x \) is the independent variable.

Step2: Compare with the given function

The given function is \( f(x)=100\cdot1.7^x \). We can rewrite \( 1.7 \) as \( 1 + r \), so \( 1 + r = 1.7 \).

Step3: Solve for the growth rate \( r \)

Subtract 1 from both sides: \( r=1.7 - 1=0.7 \). To convert this decimal to a percentage, we multiply by 100, so \( r = 0.7\times100\% = 70\% \). This means the function shows a 70% growth rate.

Answer:

The percent rate of change shows 70% growth.