Question

The table below shows the value of a car during certain years . Using an exponential model , write an equation for the curve of best fit, then estimate the value of the car in 2016 .​

Answer 1

The exponential function that gives the value of the car in t years after 2008 is:

$A(t) = 27500(0.88)^t$.

Using the function, the estimate for the value of the car in 2016 is of $9,900.

What is an exponential function?

A decaying exponential function is modeled by:

$A(t) = A(0)(1 - r)^t$

In which:

• A(0) is the initial value.

• r is the decay rate, as a decimal.

In this problem:

• The initial value is of A(0) = 27,500.

• Considering the first year change, we have that 1 - r = 24200/27500 = 0.88.

Hence, the equation is:

$A(t) = 27500(0.88)^t$

2016 is 8 years after 2008, hence the value of the car will be given by:

$A(8) = 27500(0.88)^8 = 9900$

More can be learned about exponential functions at brainly.com/question/25537936

Answer 2

The exponential function is given as y = 27500(0.88)ˣ and the value of the car in 2016 is $9890

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the value of the car after x years after 2008, hence:

at x = 0, y = 27500

27500 = ab⁰

a = 27500

At x = 1, y = 24200, hence:

24200 = 27500b¹

b = 0.88

y = 27500(0.88)ˣ

In 2016, x = 8, hence:

y = 27500(0.88)⁸ = 9890

The exponential function is given as y = 27500(0.88)ˣ and the value of the car in 2016 is $9890

Find out more on equation at: brainly.com/question/2972832