Common Core Math IINameDate
Exponential Functions Review
1)You place $500 in a savings account. The bank will give you interest on your money at a MONTHLY rate of 0.5%. How much money will be in the account at the end of 2 years?
Remember: .
b. If the interest is compounded quarterly, how much money will be in the account after 2 years?
2)The function y = 290,000 (0.92)x represents the value of an home.
a. Is the value of the home growing or decaying?
b. What is the percentage of growth or decay?
3)Use your calculator to find the following logarithms.
- log25b. log4.26 c. log 10 d. log (0.01) e. log 345
4)Use your knowledge of exponents and logarithms to solve these equations two ways.
- -3(10x) = - 3,000b. 102x-1 = 1000c. 102x-3 = 200d. 10x = 10
5)A 50 milligram sample of Carbon-10 has a half-life of 30 seconds. Write an exponential function to model its decay. Let x= time in seconds and f(x) = the amount of Carbon-10 remaining in the sample. Find the amount of substance after 3 minutes?
6)Aunpopular antique is gaining value because it is so hard to find. In 1985 its value was $200, and in 2000 its value was $50.
- Find an explicit exponential function to model the information – show your work.
- Write a recursive (NOW-NEXT) function to model the data.
- Determine the percentage of yearly depreciation .
- If the same trend continues, how much was the antique worth in 2010?
Use what you know about solving exponential equations with base 10 to solve the following growth problem.
7)In a drop of pond water, there are 18 protozoa. Ten hours later, there are 180 protozoa in the dish. P(t) = 18(100.1t) provides an exponential growth model that matches these data points.
- Verify that the model P(2) is approximately 28.5 .
- Use the given function to estimate the time when the bacteria population would be expected to reach 200,000.
8)For the function f(x) = (2.75)x - 1 evaluate the following:
- f(-1) =
- f(0) =
- f(5) =
- f(2) =
9) For each of the functions describe the key characteristics.
y = 10x-2 +4 / y = -log(x-6)Domain
Range
Asymptotes
Zeros (x-intercept)
y-intercept
Sketch of the function
10) What is the inverse of the function:
- ,b. c. f(x) = 8 + 4xd. f(x) =
The following table gives some ordered pairs generated using the function g(x). Create a table containing points from g-1(x).
x / g(x) / x / g-1(x)6 / 4
2 / 0
0 / -2
-8 / -10
Explain how you created this table.
11. A population of 50 rabbits triples every 2 years.
a) Write an equation to model this.
b) How many rabbits are in the population in 10 years?
12. The value of a car depreciates 7% every year. The car originally has a value of $21,999.
a) Write an equation to model this.
b) What is the value of the car in 14 years?
13. Suppose a manufacturer invented a computer chip in 1978 that had a computational speed of 2. The company improves its chip so that every 3 years, the chip doubles in speed. What would the chip’s speed have been for the year 2002?