Chapter 9.9, Problem 17PPS

(a)

To determine

To calculate: To graph the function and identify y-intercept and also explain its meaning.

Answer to Problem 17PPS

y-intercept is $1000$ , that means that the initial amount deposited in the account is $1000$

Explanation of Solution

Given information: J opened a savings account with an interest rate of $5\%$ . The balance of his account is represented by the function $y=1000{\left(1.05\right)}^x$ , where $x$ represents the number of years the money has been in the account

Calculation:

Given that the balance of his account is represented by the function $y=1000{\left(1.05\right)}^x$ , where $x$ represents the number of years the money has been in the account

When $x=1$

  $\begin{array}{l}y=1000{\left(1.05\right)}^1\\ y=1050\end{array}$

When $x=2$

  $\begin{array}{l}y=1000{\left(1.05\right)}^2\\ y=1000\left(1.1025\right)\\ y=1102.50\end{array}$

When $x=3$

  $\begin{array}{l}y=1000{\left(1.05\right)}^3\\ y=1000\left(1.157625\right)\\ y=1157.625\end{array}$

Plotting the points on graph:

  

y-intercept is calculated by substituting $x=0$

  $\begin{array}{l}y=1000{\left(1.05\right)}^0\\ y=1000\left(1\right)\\ y=1000\end{array}$

This means that the initial amount deposited in the account is $1000$

Conclusion:

Hence, graph is sketched, y-intercept is $1000$

(c)

To determine

To calculate: To find after how many years will the balance be greater than $\$2000$

Answer to Problem 17PPS

The amount will be more than $\$2000$ after $14.25$ years

Explanation of Solution

Given information: J opened a savings account with an interest rate of $5\%$ . The balance of his account is represented by the function $y=1000{\left(1.05\right)}^x$ , where $x$ represents the number of years the money has been in the account

Calculation:

Given that the balance of his account is represented by the function $y=1000{\left(1.05\right)}^x$ , where $x$ represents the number of years the money has been in the account

Graph of function is as follows:

  

From the graph, after $14.25$ years the amount will be more than $\$2000$

Conclusion:

Hence, after $14.25$ years