PRECALCULUS:GRAPHICAL,...-NASTA ED.

10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

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Expert Solution & Answer

Chapter P.4, Problem 46E

Solution

a.

The possible value of x in the given situation.

0≤x≤18 000

Given:

The person plans to invest $18 000 , putting part of the money x into a savings account that pays 5% annually and the rest into an account that pays 8% annually.

Calculation:

Since the person can invest 0 dollars to $18 000 in any of the account, the possible value for x could be any real number between 0 and 18000.

Thus, the possible values for x are 0≤x≤18 000 .

b.

The equation if the person invested x dollars at 5% and rest on the other account that pays 8% at the end of one year.

I=0.05x+0.0818 000−x

Given:

The person plans to invest $18 000 , putting part of the money x into a savings account that pays 5% annually and the rest into an account that pays 8% annually.

Concept Used:

The interest formula is given by, I=P⋅r⋅t, where P is the principal amount, r is the rate of interest in decimals and t is the time.

Calculation:

Since x dollars invested in the account paying 5% interest, the amount invested in the account paying 8% is 18 000−x .

So, the interest earned from both accounts at the end of one year is

Total interest=interest from 5% account+interset from 8% account=x⋅0.05⋅1+18000−x⋅0.08⋅1=0.05x+0.0818000−x

Thus, the total interest earned from both accounts at the end of one year is I=0.05x+0.0818 000−x .

c.

The amount invested at 5% if she earned a total $1020 at the end of first year.

x=$14 000

Given:

The person plans to invest $18 000 , putting part of the money x into a savings account that pays 5% annually and the rest into an account that pays 8% annually.

Calculation:

In order to find the amount invested at 5% account, plot the graph of the function I=0.05x+0.0818 000−x and draw a horizontal line at I=1020 as shown below

Thus, the amount invested in 5% account is $14 000 .

d.

The amount invested at 5% if she earned a total $1185 at the end of first year.

x=$8500

Given:

The person plans to invest $18 000 , putting part of the money x into a savings account that pays 5% annually and the rest into an account that pays 8% annually.

Calculation:

In order to find the amount invested at 5% account, plot the graph of the function I=0.05x+0.0818 000−x and draw a horizontal line at I=1185 as shown below

Thus, the amount invested at 5% account is x=$8500 .

Chapter P.4, Problem 45E

Chapter P.4, Problem 47E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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Solution Summary: The author calculates the possible value of x in the given situation. The person invests 18000 in a savings account that pays 5% annually and the rest in an account paying 8% annually

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Chapter P Solutions