Question

during a 10 - year period of constant inflation, the value of a $500,000 property will increase. according to the equation, $v = 500,000e^{0.04t}$, where v is the value of the property and t is the time in years, what will the value of the property be in 8 years? the value of the property in 8 years will be $709,858.34. (round to the nearest cent as needed.)

Explanation:

Step1: Substitute \(t = 8\) into the formula

Given \(v=500000e^{0.04t}\), when \(t = 8\), we have \(v = 500000e^{0.04\times8}\).

Step2: Calculate the exponent

First, calculate \(0.04\times8=0.32\). So the formula becomes \(v = 500000e^{0.32}\).

Step3: Evaluate \(e^{0.32}\)

Using a calculator, \(e^{0.32}\approx1.3771277\).

Step4: Calculate the value of \(v\)

Then \(v=500000\times1.3771277 = 709858.35\approx709858.34\) (rounded to the nearest cent).

Answer:

$709858.34$