BCCCMAT 128

Summer 2020

Professor: Ray Orocco-John

Student’s Name: ________________________________________________

Test #4

Show all work. Answers without adequate justification will not receive full credit. Solve problems

algebraically whenever possible. Simplify to the lowest terms and underline all final answers.

1) (6pts) Match the graphs with the equations.

y = 3x

Letter _________

E

F

y = (0.4) x Letter _________

D

C

B

y=e

x

A

Letter _________

y = log x

Letter ________

y = ln x

Letter _________

y = 2x

Letter _________

2) (8pts) Fill in the blanks in the following table:

Function

y-intercept

Growth or decay rate

(0, 22)

Growth or

decay?

Decay

(0, 7)

Growth

4% continuous rate

8% annual rate

y = 16(1.3) x

y = 13e0.45 x

3) (5pts) Granny wants to start a college account for her newborn granddaughter. How much money does she

need to deposit now into an account earning 3% compounded quarterly so it will be worth $30,000 in 18

years?

4) (9pts) The population, P, of a group of rabbits t years after being released in a new habitat is given by

t

P (t ) = 600 (1.04 )

a) How many rabbits were initially released?

b) Fill in the blank: The rabbit population is growing by _____% per year

c) How many rabbits will there be in 2 years?

d) When there will be 700 rabbits?

5) (15pts) Solve the following for x.

a) 2log3 ( 2 x − 5) = 4

b) 3(4) x+ 2 = 18

c) 4e8 x + 3 = 19

d) 53x-2 = 1252x

e) 32x-2 = 64

6) (5pts) Find a formula for an exponential function such that f(-1) = 12 and f(1) = 3

7) (3pts) Rewrite as a single logarithm: 3log( x) + 4 log( y ) − log( z )

8) (3pts) Solve for x. log( x + 48) + log( x) = 2

9) (5pts) Bismuth-214 has a half-life of 20 minutes. What percent of the original amount is left after one hour?

10) (6pts) In 2003, there were 7225 Starbucks stores. In 2006, there were 12,440 Starbucks stores. If Starbucks

continues to increase exponentially at the same rate find the doubling time.

11) (6pts) The Island of Niue is currently home to 5000 people, and the population has been growing

continuously by 9 %. The Cook Islands are currently home to 20,000 natives but the native population has

been continuously decreasing by 5 % each year.

Write the equation for the population of the Island of Niue. N(t) = __________________________

Write the equation for the population of the Cook Islands. C(t) = __________________________

If these trends continue, during what year will the populations be the same?

12) (8pts)

If 7000 dollars is invested in a bank account at an interest rate of 6 per cent per year,

a. Find the amount in the bank after 12 years if interest is compounded annually:

b. Find the amount in the bank after 12 years if interest is compounded quarterly:

c. Find the amount in the bank after 12 years if interest is compounded monthly:

d. Finally, find the amount in the bank after 12 years if interest is compounded continuously:

13) (4pts) Write an equation for the exponential graph below:

14) (12pts) The count in a bacteria culture was 700 after 15 minutes and 1100 after 40 minutes. Assuming the

count grows exponentially.

a. What was the initial size of the culture?

b. Find the doubling period.

c. Find the population after 60 minutes.

d. When will the population reach 13000?

15) (5pts) The 1906 San Francisco earthquake had a magnitude of 7.9 on the MMS scale. Later there was an

earthquake with magnitude 4.7 that caused only minor damage. How many times more intense was the San

Francisco earthquake than the second one?

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