Question

1. $f(x) = -3left(\frac{1}{4}\

ight)^x$
growth or decay?
initial value:
growth/decay factor:
growth/decay rate:

Explanation:

Step1: Identify growth/decay

An exponential function has the form $f(x)=a(b)^x$. If $0

Step2: Find initial value

Initial value is $a$ (when $x=0$, $b^0=1$). Here $a=-3$.

Step3: Find decay factor

Decay factor is $b$ from $f(x)=a(b)^x$. So $b=\frac{1}{4}$.

Step4: Calculate decay rate

Decay rate = $1 - b$.
$\text{Rate} = 1 - \frac{1}{4} = \frac{3}{4} = 0.75 = 75\%$

Answer:

Growth or Decay? Decay
Initial value: $-3$
Growth/Decay Factor: $\frac{1}{4}$
Growth/Decay Rate: $75\%$ (or $0.75$)