the value of a collectors item is expected to increase exponentially each year. the item is purchased for…

the value of a collectors item is expected to increase exponentially each year. the item is purchased for $500 and its value increases at a rate of 5% per year. find the value of the item after 4 years.\n$578.81\n$607.75\n$1687.50\n$2531.25

the value of a collectors item is expected to increase exponentially each year. the item is purchased for $500 and its value increases at a rate of 5% per year. find the value of the item after 4 years.\n$578.81\n$607.75\n$1687.50\n$2531.25

Answer

Explanation:

Step1: Identify the formula

The compound - interest formula for exponential growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the annual interest rate (as a decimal), and $t$ is the number of years.

Step2: Convert the percentage to a decimal

Given $r = 5%=0.05$, $P = 500$, and $t = 4$.

Step3: Substitute the values into the formula

$A=500\times(1 + 0.05)^4$. First, calculate $(1 + 0.05)^4=(1.05)^4 = 1.05\times1.05\times1.05\times1.05=1.21550625$. Then, $A = 500\times1.21550625=607.753125\approx607.75$.

Answer:

$607.75$ (corresponding to the option $$607.75$)