Exercise 10 Page 322

Practice makes perfect

We will use the Compound Interest Formula to write the function A(t) that represent the balance after t years. We deposit $ 750 in a savings account that earns 5 % annual interest compounded quarterly. Then, P= 750, r= 0.05, and n=4.

y= P(1+r/n)^(nt) ⇒ A(t)= 750(1+0.05/4)^(4t) Let's simplify it.

A(t)=750(1+0.05/4)^(4t)

CalcQuot

Calculate quotient

A(t)=750(1+0.0125)^(4t)

AddTerms

Add terms

A(t)=750(1.0125)^(4t)

The function A(t) represents the balance after t years.

To find the balance after 4 years, we will substitute 4 for t in the function we write in Part A.

A(t)=750(1.0125)^(4t)

Substitute

t= 4

A( 4)=750(1.0125)^(4( 4))

▼

Simplify right-hand side

Multiply

A(4)=750(1.0125)^(16)

CalcPow

Calculate power

A(4)=750(1.219889 ...)

Multiply

A(4)=914.917160 ...

RoundDec

Round to 2 decimal place(s)

A(4)=914.92

The balance after 4 years is $914.92.

Subchapter links

1 Exponential Functions p.322

2 Exponential Growth and Decay p.322

3 Comparing Linear and Exponential Functions p.323

4 Solving Exponential Equations p.323

5 Geometric Sequences p.324

6 Recursively Defined Sequences p.324

Exercise 10 Page 322

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