Math 10024 Test 1 Review Problems
(1.1)
Factor out the common term with the lesser power and write in factored form. Write your answers with positive exponents only.
1. 2.
3.4.
(1.2)
Factor out the GCF or any common factors including binomial factors to the lesser power. Write your answers using only positive exponents.
5. 6.
7.
(1.3)
Solve the equations.
8.9.
Solve the inequalities. Write your answer using interval notation.
10.11.
(2.1)
12. Write a formula for an exponential function with an initial value of 250 and
a) growth factor of 1.10 b) growth rate of 5.5% c) decay rate of 7.5%
13. How much money would be in an account after 15 years if you deposited $1,500 at 6.5% compounded
a) annually b) quarterly c) monthly d) daily
14. Find the effective annual yield for an account which compounds interest 3.5% daily.
15. Explain why in the formula the variable C represents the beginning amount of your quantity, given that the variable t represents time.
16. Suppose that you need $5,000 in 3 years and found an account that will give you 7% compounded quarterly. How much would you need to invest now so that you will have that $5,000 in 3 years?
(2.2)
Identify each of the following as a growth or decay exponential function. Identify the growth or decay factor, rate, and the initial value.
17.18.19.
20.21.22.
23. How many people would live in a town after 8 years if 10,000 people lived there originally and 1.5% left
town every year?
24. The amount (in milligrams) of a drug in the body t hours after taking a pill is given by
.
a)What is the initial dose given?
b)What percent of the drug leaves the body each hour?
c)What is the amount of the drug left after 10 hours?
25. Write a formula for an exponential function with an initial value of 5,000 and halving every time period.
(2.3)
For the following functions, sketch the graph and characterize the graph of each, naming domain, range, initial value (y-intercept), end behavior, and horizontal asymptote.
26.27.
28.29.
(2.4)
30. How much money is in an account after 8 years if you deposit $1200 and the account gives 4.5%
compounded continuously?
31. How much would you need to invest now in an account that gives 3.5% compounded continuously if you want to have $2,000 in 5 years?
32. Which is the better deal: an account that pays 4% compounded daily or one that pays 3.95% compounded continuously?
33. The number of people in a small population after t years is given by
a) Is the population growing or shrinking?
b) What is the initial number in the population?
c) How large is the population after 10 years?
34. The number of people in a larger population after t years is given by
a) Is the population growing or shrinking?
b) What is the initial number in the population?
c) How large is the population after 10 years?
(2.5)
Solve the following equations.
35.36.37.
38.39.40.
Answers
1.
2.
3.
4.
5.
6.
7.
8. or
9. or
10.
11.
12.a)
b)
c)
13.a) $3857.76
b) $3945.71
c) $3966.30
d) $3976.41
14. 3.56%
15. Since , then, at the beginning, , and
16. $4060.29
factor / rate / In. Val17. / growth / 1.02 / 2% / 10
18. / decay / 0.75 / 25% / 300
19. / decay / 1 / 3 / % / 5
20. / growth / 5 / 400% / 1
21. / growth / 4 / 300% / 0.5
22. / decay / 1 / 8 / 87.5% / 15
23. 8861
24. a) 25 b) 15% c) 4.92
25.
domain / range / in.val / end
behavior / asym
26 / / / / /
27 / / / 3 / /
28 / / / / /
29 / / / / /
30. $1720
31. $1678.91
32. 4% compounded daily
33.a) growing b) 5000 c) 27,158,297
34. a) shrinking b) 20,000 c) 377
35.
36.
37. or
38.
39.
40.