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. multiple choice 10 points $607.75 $578.81 $2531.25 $1687.50

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. multiple choice 10 points $607.75 $578.81 $2531.25 $1687.50

Answer

Explanation:

Step1: Recall the compound - interest formula for exponential growth

The formula for exponential growth of an asset's value is $A = P(1 + r)^t$, where $P$ is the initial value, $r$ is the annual growth rate as a decimal, and $t$ is the number of years.

Step2: Identify the values of $P$, $r$, and $t$

Given that $P=$500$, $r = 0.05$ (since $5%=0.05$), 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\approx$607.75$.

Answer:

$$607.75$