Chapter 7 Review

Multiplying Exponents

100

−16x⁵y³(−12)

192x⁵y³

200

x²(3y³)

3x²y³

300

14x⁴y⁵(−13xy³)

−182x⁵y⁸

400

−14x³y³(16x³)

−224x⁶y³

500

−14x²y³(5x²y³)

−70x⁴y⁶

Dividing Exponents

100

21x⁴y⁶ / 35x⁴y⁴

3y² / 5

200

24x⁷y⁷ / 40xy⁶

3x⁶y¹ / 5

300

30x⁴y⁶ / 20x³y²

3xy⁴ / 2

400

27x⁸y⁵ / 9x⁴y⁵

 3x⁴

500

3x⁸y⁷ / 6x⁶y³

 1x²y⁴ / 2

Growth Functions

100

What is the general form of an exponential growth equation?

y=a(1+r)^x

200

If a population starts at 500 and grows at a rate of 4% per year, what is the growth equation?

y=500(1+0.04)^x

300

In the equation y=1200(1+.06)^x, what does the 1.06 represent?

the growth factor (or 6% growth rate)

400

How many years will it take for an investment of $1,000 to grow to $2,000 at a 5% annual growth rate? (Round to the nearest year)

About 15 years

500

A bacteria culture triples every 7 hours. Write the growth equation if the starting amount is 80.

y=80(3)^x/7

Decay Functions

100

What is the general form of an exponential decay equation?

y=a(1−r)^x

200

A car’s value is $20,000 and it loses 10% each year. What is the decay equation?

y=20000(1−0.10)^x or y=20000(0.90)^x

300

In the equation y=1500(0.85)^x, what does 0.85 represent?

the decay factor (or 15% decay rate)

400

A phone loses 30% of its value each year. How much will a $600 phone be worth in 3 years?

$205.80

500

A radioactive substance halves every 12 hours. Write a decay equation starting with 100 grams.

y=100(0.5)^t/12

Compound Interest

100

What is the formula for compound interest?

A=P(1+r/n)^n*x

200

You invest $1,000 at 5% annual interest, compounded yearly. What is the equation?

A=1000(1+0.05/1)^1*x or A=1000(1.05)^x

300

If interest is compounded quarterly, what does “n” equal in the formula?

4

400

You invest $2,500 at 6% interest, compounded monthly for 3 years. What is the amount? (Round to nearest cent)

$2,993.48

500

A bank compounds interest daily. You invest $3,000 at 4.5% for 5 years. What is the final amount?

$3,762.89