Question

1. $f(x) = 25\left(\frac{1}{2}\

ight)^x$\
growth or decay? \underline{\qquad}\
initial value: \underline{\qquad}\
growth/decay factor: \underline{\qquad}\
growth/decay rate: \underline{\qquad}

Explanation:

Step1: Identify growth/decay

The exponential function is in the form $f(x)=a(b)^x$. If $0

Step2: Find initial value

Initial value is $a$ in $f(x)=a(b)^x$. Here $a=25$, so initial value is 25.

Step3: Find decay factor

Decay factor is $b$ in $f(x)=a(b)^x$. Here $b=\frac{1}{2}$, so decay factor is $\frac{1}{2}$.

Step4: Calculate decay rate

Decay rate $r = 1 - b$. Substitute $b=\frac{1}{2}$:
$r = 1 - \frac{1}{2} = \frac{1}{2} = 50\%$

Answer:

Growth or Decay? Decay
Initial value: 25
Growth/Decay Factor: $\frac{1}{2}$
Growth/Decay Rate: 50% (or $\frac{1}{2}$)