Question

two years ago, marc bought a new cell phone. his purchase price was $750. the value of the phone for the next 2 years was $637.50 and $541.88, respectively. find the exponential function that represents the value of marcs phone t years after it was purchased. (1 point)

○ $f(t)=637.50 - 0.85^{t}$
○ $f(t)=750 - 0.85t$
○ $f(t)=750cdot1.15^{t}$
○ $f(t)=750cdot0.85^{t}$

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - decay function is $f(t)=a\cdot b^{t}$, where $a$ is the initial value and $b$ is the decay factor ($0 < b<1$). Here, the initial value $a = 750$ (the purchase price of the phone).

Step2: Calculate the decay factor

Let's use the value of the phone at $t = 1$. We know that when $t = 1$, $f(1)=637.50$. Substitute $a = 750$ and $t = 1$ into $f(t)=a\cdot b^{t}$:
\[637.50=750\cdot b^{1}\]
\[b=\frac{637.50}{750}=0.85\]
So the exponential function that represents the value of the phone $t$ years after it was purchased is $f(t)=750\cdot0.85^{t}$.

Answer:

$f(t)=750\cdot0.85^{t}$