The expression 210,000\left(1.02\right)^x210,000(1.02)

x

models the estimated home value after x years. Which statement is the correct representation of the 1.02 in the expression?




The house has a starting value of 1.02.



The house is decreasing in value by 2% each year.



The house is increasing in value by 2% each year.



The value of the house is changing by 0.02% each year.

Respuesta :

Answer:

The house is increasing in value by 2% each year.

Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:

[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]

Step-by-step explanation:

For this case if we have this expression

[tex] 210000(1.02)^x[/tex]

We have the same functional forma like the exponential model given by:

[tex] y = a b^x[/tex]

Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.

So let's analyze the possible options:

The house has a starting value of 1.02.

False the starting value for this case is 210000 since if x=0 then we see that the value is 210000

The house is decreasing in value by 2% each year.

False the increase is 1.02 each year so then in % we have

[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]

We  have an increase of 2% each year

The house is increasing in value by 2% each year.

Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:

[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]

The value of the house is changing by 0.02% each year.

False the increase is 2% per year

Q&A Education