Name: TEST REVIEW
Answers are in red.
1) Which of the following are exponential functions? For those that are exponential, state the initial value and the base.
a) y = x6 no b) y = 5x yes, a = 1, b = 5 c) y = 35 no d) y = 4 · 6x yes, a = 4, b = 6
2) Determine the formula for an exponential function containing the points (0, 3) and (1, 1).
y = 3(1/3)x
3) Describe how to transform f(x) = 6x to g(x) = 6-x + 3. Sketch the graph. Left 3, Reflect over y-axis.
4) Is P(t) = 5.2 · 1.023t and exponential growth or decay function? Growth
5) Determine the exponential function that…
a) …has an initial value of 5 and decreases at a rate of 3% each week. y = 5(0.7)x
b) …has an initial value of 325 and doubles every month. y = 325(2)x
c) …has an initial value of 210 and halves every month? y = 210(1/2)x
6) The 2000 population of Malden, MA was 55,765. If the population increased at a rate of 1.94% each year, how many people live in Malden today? 70,225.891
7) The half-life of a certain radioactive substance is 12 days. There are 4.3 g present initially. When will there be 3.22 g left? 5 days
8) Solve for x:
a) log464 = x 3 b) log2x = 4 16 c) log9x = ½ 3 d) log(-2) = x DNE
e) ln 0.325 = x -1.124 f) logx25 = 2 5 g) logx = -2 0.01 h) xlog102 = 18 9
i) lne3x = 27 9 j) 3lne4 = x 12 k) 5x = 10 1.431 l) 3e2x + 4 = 9 0.255
m) 73x – 1 = 15 0.797 n) 1.05x = 3 22.517 o) lnx = 5.4 221.406 p) logx3 = 5 46.416
9) Use the change-of-base formula and your calculator to evaluate the logarithm: log12259. 2.236
10) Write log4x using only natural logs. lnx/ln4
11) Write log9x using only common logarithms. logx/log9
12) Suppose a $4000 principal was invested at 6% interest rate compounded annually and yields $5353. For how many years was it invested? 5 years
13) The number P of students infected with the flu at Northridge High School t days after exposure is modeled by
P(t) = 300
1 + e4 – t
a) What was the initial number of students infected with the flu? 5.396
b) How many students were infected after 3 days? 80.682
c) When will 100 students be infected? 3.307
d) What is the maximum number of students that could be infected? 300
14) Find the amount A accumulated after investing principal P = $450 for 3 years at an interest rate of 4.6% compounded semi-annually. $481.77
15) The population of Preston, Ohio is 89,000 (now in 2012) and is decreasing by 1.8% each year. Predict when the population will be 50,000. 31.745 years, in the year 2043
16) If Joe invests $12,500 into a retirement account with interest compounded continuously and the value of his account triples in 18 years, what was the interest rate? r = 0.061, 6.1%