Question

State whether the decay is linear or​ exponential, and answer the associated question. The value of a car is decreasing by 9​% per year. If the car is worth ​$11 comma 000 ​today, what will it be worth in two​ years? g

Answer 1

Answer:

• Exponential
• A(2)=$9109.10

Step-by-step explanation:

Since the value of the car decreases by a common factor each year, the decay is exponential.

An exponential decay function is of the form

$A(t)=A_0(1-r)^t where:\\Initial Value, A_0=\ 11,000\\ Decay Factor, r=9%=0.09$

Therefore, the function modeling the car's decay is:

$A(t)=11000(1-0.09)^t$

We want to determine the car's value in two years.

When t=2

$A(2)=11000(1-0.09)^2\\A(2)=\ 9109.10$

The value of the car in 2 years will be A(t)=$9109.10

Answer 2

Final value of the car after 2 years will be $9109.10

 Value of the car decay by 9%.

Since, 9% is a common factor by which the value of car is decreasing,

Therefore, decay will be exponential.

Expression for the exponential decay is given by,

$P=P_0(1-\frac{r}{100} )^t$

Here, $P=$ Final price

$P_0=$ Initial price

$r=$ Rate of decay

$t=$ time

  If initial price of the car $P_0=11000$, rate of decay $r=0.09$ and $t=$ Number of years

By substituting the values in the expression,

P = $11000(1-0.09)^2$

  = 11000(0.91)²

  = $9109.10

   Therefore, final value of the car after 2 years will be $9109.10

Learn more,

https://brainly.com/question/24515212