Chapter 9.8, Problem 28PPS

a.

To determine

To determine which kind of function models the data.

Answer to Problem 28PPS

Exponential function model the data.

Explanation of Solution

Given information:

  

Exponential function model the data

  $f(t)=a{(b)}^t$

where a is initial price

  $b=1+r$

r is rate of depreciation in price

t is time in years

  $f(t)$is depreciation in price in t years

Hence, exponential function model the data.

b.

To determine

To write equation of function that model the data.

Answer to Problem 28PPS

  $f(t)=a{(b)}^t$

Explanation of Solution

Given information:

  

Exponential function model the data

  $f(t)=a{(b)}^t$

where a is initial price

  $b=1+r$

r is rate of depreciation in price

t is time in years

  $f(t)$is depreciation in price in t years

Hence, exponential function model the data.

c.

To determine

To write equation of function that model the data.

Answer to Problem 28PPS

$6437.

Explanation of Solution

Given information:

  

Formula used:

  $f(t)=a{(b)}^t$

  $b=1+r$

Exponential function model the data

  $f(t)=a{(b)}^t$

where a is initial price

  $b=1+r$

r is rate of depreciation in price

Finding rate

  $P=18500$

Amount( A ) in 1 years $=15910$

  $t=1$

Using formula

  $15910=18500{(1+\frac{r}{100})}^1$

On solving,

  $2590=18500\times \frac{r}{100}$

On solving,

  $r=0.14$

Price after 7 years

  $t=7$

  $a=18500$

  $b=1+0.14$

On solving,

  $b=1.04$

Using formula

  $f(7)=18500{(1.04)}^7$

On solving,

  $f(7)=\$6437$