precalculus exam

153_ch_5_take_home_test.pdf

Pre-calc 153 Chapter Five Take Home Test Name _______________________ YOU MUST SHOW YOUR WORK! Test is due Monday at 12 noon.

1. f(x) = 0.5(2x), g(x) = 5x-‐12, and h(x) = {(4, -‐1), (3, 2), (1, 4), (-‐1, 4)}. a. Determine g(f(0).

b. Determine (f°g)(x).

c. Determine h-‐1(x).

d. Determine g-‐1(x).

e. Determine (f°h)(x).

f. Graph f(x).

g. Explain why f(x) is one-‐ to-‐one.

h. Determine f-‐1(x)

a. b. c. d. e.

g. h.

2. Evaluate the following in exact values: a. (1/3)log(1/5)(125)

b. eln 2π

c. log 10e

a. b. c.

3. Solve for x in each: a. 92x+3 = 812x-‐1

€

log 5 x = 6

a. b.

c. 2 log 2x = log (7x-‐3)

d. 7•3(x+2) = 5x

e. log3 (x+1) + log3 (x+6) = 2.

c. d. e.

4. Assume there is a radioactive isotope that decays according to A(t)=A0ekt where A0 is the initial amount and t is in years. a. Determine k if five

grams decays to two grams in 12 years.

b. If you started with fifteen grams, how much is still radioactive after 20 years?

c. In how many years will 20% be still radioactive?

d. What is the half-‐ life of this isotope?

a. b. c. d.

5. $600 is invested in an account that is compounded monthly (A(t)=A0(1+r/n)nt) at an interest rate of 4%. a. How much is in

the account after ten years?

b. How long will it take for the balance to grow to $1000?

c. How long for the balance to double?

a. b. c.