Question

Sheryl purchased a plot of land for $32,500. The land appreciates about 4.9% each year. What is the value of the land after eleven years? (3 points)

Select one:
a. $50,017.50
b. $18,701.18
c. $55.006.46
d. $33,989.96

Answer 1

The value of the land after eleven years is:

Option: C

C. $ 55006.46

Explanation:

Sheryl purchased a plot of land for $32,500. The land appreciates about 4.9% each year.

i.e. the cost of the land is increasing by a rate pf 4.9% each year.

Now, we can model this situation with the help of a exponential function which is given by:

`f(x)=ab^x`

where a is the initial amount.

and b is the change.

where b=1+r , r is the rate of increase.

Here r= 4.9%=0.049

Hence, b=1.049

Also, a= 32,500

Hence, the cost of land after x years is given by:

`f(x)=32500(1.049)^x`

Now, we are asked to find the value of the land after eleven years.

i.e. when x=11

`f(11)=32500(1.049)^(11)\\\\f(11)=55006.46`

Answer 2

So first, if we put this into equation form it will be y = 32,500(1.049)^11 because y is the value after 3 years, 32,500 is the original price, 1.049 is the constant multiplier, and 11 is the number of years passed. Now put this into a calculator to solve to get C, $55,006.46. Hope this helps!