Question

-Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has

Answer 1

The value of home today is $ 424527.63

Solution:

Given that, Twenty years ago, Mr. Davis purchased his home for $160,000

Since then, the value of the home has  increased about 5% per year

To find: Exponential function to find the value of home today

The exponential growth function is given by:

$y = a(1 + r)^t$

Where, "y" is the worth after "t" years

"a" is the initial amount

"r" is the rate of interest per year

From given information,

a = 160000

t = 20 years

$r = 5 \% = \frac{5}{100} = 0.05$

Substituting the values we get,

$y = 160000(1 + 0.05)^{20}$

Thus the exponential function is found

Let us find the value

$y = 160000(1 + 0.05)^{20}\\\\y = 160000(1.05)^{20}\\\\y = 160000 \times 2.653\\\\y = 424527.63$

Thus the value of home today is $ 424527.63