ReviewChapters 4 & 8

Topics

How numbers deceive (3E) Simple Interest Compound interest APY Savings plan Loan Payments Growth: Linear vs Exponential Real population Growth Logarithmic Scales

1. How much could you save if you purchased a $1000 5-year savings certificate that paid 5% compounded quarterly?

4 5.054$1000 1 $1282.04A

2. What is the value after 15 years if you deposit $5000 for your child’s education and the interest is guaranteed at 16% compounded continuously?

.16 15

2.4

$5000

$5000

$55,115.88

A e

e

3. Suppose that you invest $2000 in an account with an APR of 5.9% compounded daily. What is the APY?

After one year, you have:

So your APY is

365.059365$2000(1 ) $2121.54A

$2121.54 $2000100%

$20006.077%

APY

4. Suppose a sobriety test is 95% accurate. Of the 1000 drinking drivers tested, only 75 actually were above the legal limit. Complete the table below. What percent of the legally intoxicated drivers were not identified by the sobriety test?

drunk ‘not drunk’ Total

Sobriety test +

Sobriety test –

Total 1,000

4. Suppose a sobriety test is 95% accurate. Of the 1000 drinking drivers tested, only 75 actually were above the legal limit. Complete the table below. What percent of the legally intoxicated drivers were not identified by the sobriety test?

drunk ‘not drunk’ Total

Sobriety test +

71 46 117

Sobriety test –

4 879 883

Total 75 925 1,000

475 100% 5.33%

5. Suppose you see a car with an advertised price of $18,490 with payments of $480 per month for 5 years. How much total interest would you pay?

12 $480 5 $28,800Total paid

$28,800 $18,490 $10,310Interest paid

6. Suppose you have a balance of $3200 on a credit card that charges an APR of 21% compounded monthly. If you want to repay the balance in 2 years, how much should you pay each month? Assume that you charge no additional expenses to the card. How much total interest did you pay?

.211224.21

12

$3200$164.43

1 1PMT

interest 12 $164.43 2 $3200 $746.32

7. The price of a 3-day cruise is $1200 and increases at a constant rate of $60 per year. How much will the cruise cost in 4.5 years?

Linear growth:

cost $1200 60 4.5 $1470

8. In 1995 the enrollment at a certain university was 2100 students. If the enrollment increases by 8% per year, what will the enrollment be in the year 2012?

Exponential growth172100 (1 .08) 7,770enrollment

9. In 1990 the enrollment at a different university was 2200 students. If the enrollment decreases by 6% per year, what will the enrollment be in the year 2010?

Exponential decay

202200 (1 .06) 638enrollment

10. Suppose a country currently has a population of 21 million and an annual growth rate of 4.20%. If the population growth follows a logistic model with a carrying capacity of 83 million, calculate the growth rate when the population is 32 million.

3283.042 1 .025

2.5%

growth rate

11. Compare the estimated energies released by the 1990 earthquake of magnitude 7.7 in Iran to the one in 1997 of magnitude 7.5.

Energy ratio =

1.5 (7.7 7.5) 1.5 (.2) .310 10 10 1.995...

1.5 7.7

1.5 7.5

25,000 101.995...

25,000 10

or

12. How much more acidic is acid rain with a pH of 3.5 than ordinary rain with a pH of 6?a) 3 times more acidic b) 316 times more acidic c) 2.5 times more acidic d) 60 times more acidic

3.5

6

10316.227

10

12. How much more acidic is acid rain with a pH of 3.5 than ordinary rain with a pH of 6?a) 3 times more acidic b) 316 times more acidic c) 2.5 times more acidic d) 60 times more acidic

3.5

6

10316.227

10