Question

PLEASE HELP ASAP

Answer 1

In this question, two houses have an initial value of $179,000, and the projected values are given in the tables for houses 1 and 2.

Part a:

If the absolute value of the change is always the same, it is linear.

If the rate is the same, it is exponential.

House 1:

We have that:

193,606.4 - 186,160 = 7446.4

201,350.66 - 193,606.40 = 7744.26

Let's try exponential:

$\frac{193,606.4}{186,160} = 1.04$

$\frac{201,350.66}{193,606.40} = 1.04$

For house 1, the rate of change is the same, and thus, it is exponential.

House 2:

212,000  - 201,000 = 201,000 - 190,000 = 11,000.

Absolute value of change is the same, so linear.

Thus, for house 1, an exponential function is used, as the rate of change is the same, and for house 2, as the absolute value of change is always the same, it is linear.

Part B

House a:

Exponential function, with initial value of $179,000, and exponential growth rate of 1.04 - 1 = 0.04. Thus:

$f_a(x) = 179000(1+0.04)^x$

$f_a(x) = 179000(1.04)^x$

House b:

Linear function, with initial value of $179,000, increasing by $11,000 each year. So

$f_b(x) = 179000 + 11000x$

Part c:

House a after 30 years:

$f_a(30) = 179000(1.04)^30 = 580,568$

House b after 30 years:

$f_b(30) = 179000 + 110000(30) = 509,000$

In 30 years, house a will have a value of $580,568, while house b will have a value of $580,568. House a will have a higher value, due to exponential growth.

For more about linear/exponential growth, you can check brainly.com/question/14983998