Respuesta :
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:
[tex]y = a(1 + r)^t[/tex]
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
[tex]r = 5 \% = \frac{5}{100} = 0.05[/tex]
Substituting the values we get,
[tex]y = 160000(1 + 0.05)^{20}[/tex]
Thus the exponential function is found
Let us find the value
[tex]y = 160000(1 + 0.05)^{20}\\\\y = 160000(1.05)^{20}\\\\y = 160000 \times 2.653\\\\y = 424527.63[/tex]
Thus the value of home today is $ 424527.63
Thr value of Mrs. Davis' home today is $424,527.63.
What is the value of Mrs Davis home?
Based on the information provided in the question, Mrs Davis home is appreciating in value.
The exponential function for calculating the value of the home today:
FV = P (1 + r)^n
- FV = Future value
- P = Present value
- R = rate of appreciation
- N = number of years
$160,000 (1.05)^20 = $424,527.63
To learn more about future value, please check: https://brainly.com/question/18760477
