Chapter 7.6, Problem 48PPE

a.

To determine

To write: a function for the value of computer that fits to the given models.

Answer to Problem 48PPE

  $P(t)=1500{\left(\frac{4}{5}\right)}^t$

Explanation of Solution

Given information:

A computer valued at $1500 loses 20% of its value each year.

Since the value of computer decreases every year by 20%, then its value after $t$ years is given by

  $\begin{array}{l}P(t)=1500{\left(1-\frac{20}{100}\right)}^t\\ \Rightarrow P(t)=1500{\left(1-\frac{1}{5}\right)}^t\\ \Rightarrow P(t)=1500{\left(\frac{4}{5}\right)}^t\end{array}$

b.

To determine

To find: the value of computer after 3 years.

Answer to Problem 48PPE

$768

Explanation of Solution

Given information:

A computer valued at $1500 loses 20% of its value each year.

Since value of computer after $t$ years is given by

  $P(t)=1500{\left(\frac{4}{5}\right)}^t$

Putting $t=3$ in above equation we get

  $P(3)=1500{\left(\frac{4}{5}\right)}^3=1500\times \frac{64}{125}=768$

Thus the value of computer after 3 years is $768.

c.

To determine

To find: after how many years the value of computer will be less than $500.

Answer to Problem 48PPE

5 years

Explanation of Solution

Given information:

A computer valued at $1500 loses 20% of its value each year.

Since value of computer after $t$ years is given by

  $P(t)=1500{\left(\frac{4}{5}\right)}^t$

Now the value of computer after 5 years will be

  $P(5)=1500{\left(\frac{4}{5}\right)}^5=491.52$

This is less than 500

Hence the value of computer will be less than $500 after 5 years.