Download 6.1 - 6.3 Review

Algebra 2/Trig
6.1 – 6.3 Review
Name: _______________________________________ Date: _____________________ HR: _______
6.1 Exponential Growth and Decay
Evaluate each expression to the nearest thousandth for the given value of x.
1 2𝑥+1
1.) (4)
𝑓𝑜𝑟 𝑥 =
1
4
𝑥
2.) (10)2+1 𝑓𝑜𝑟 𝑥 = 5
Find the multiplier for each rate of exponential growth or decay.
3.) 7.1% growth
4.) 0.14% decay
Write the exponential expression, and predict the population of bacteria for each time period.
5.) 25 bacteria that triple every 2 hours
a. After 4 hours
b. 1 hour ago
6.) 50 bacteria that double every 30 minutes
a. After 1.5 hours
b. 2 hours ago
7.) The present population of a country is 2,321,255. The population is growing at about 3% per
year. Predict the population of the country 2 years from now.
6.2 Exponential Functions
Find the final amount for each investment.
8.)
$1000 earning 5.25% interest compounded annually for 3 years.
9.)
$2500 earning 6% interest compounded quarterly for 5 years.
10.)
An initial investment made June 30, 1990 is worth $1472 on June 30, 1999, the rate of
growth is 1.8%. What is the amount of the initial investment?
11.)
A car purchased August 3, 1989 for $14,592 is worth $6872 on August 3, 2000. What is
the effective annual yield?
12.)
6.3
Find the y-intercept for f(x) = -3(2.1)x.
Logarithmic functions.
Write each equation in logarithmic form.
13.)
1 −4
(3)
= 81
13.)
1 3
(4) =
1
64
Write each equation in exponential form.
1
14.)
log 216 6 =
15.)
log 4 256 = −4
16.)
log 7 1 = 0
3
1
Solve each equation for x. Round answers to the nearest hundredth.
17.)
10𝑥 = 20
18.)
10𝑥 = 0.4
20.)
−3 = log 2 𝑛
Find the value of n in each equation.
19.)
6 = log 𝑛 64
21.)
Find the y-intercept of f(x) = 3(1.2)x.
22.)
The “effective yield” is the same as ______.