Download Exponential Functions Review Day 2

Algebra 1
Name: ___________________________________
Exponential Functions Review – Day 2
Date: __________________ Hour: ____________
Main Concepts
1. How does the value of a affect the graph and table of an exponential function?
_____________________________________________________________________
_____________________________________________________________________
2. What values of b indicate exponential growth? __________________________________
What values of b indicate exponential decay? ___________________________________
3. How do you recognize exponential growth or decay from:
A graph: ______________________________________________________________
A function rule: _________________________________________________________
A table: _______________________________________________________________
A real-world situation: ___________________________________________________
Review
1.
2.
3.
5.
4.
Evaluating Functions
Evaluate f (x) = 5 · 3x for x = 4, 5, 6.
1.
2. Evaluate f (x) = 6 · 2x for x = –3, - 2, - 1.
3.
A population of 50 bacteria in a laboratory culture doubles every 30 min.
The function y  50  2 x models the population, where x is the number of 30-min. periods.
a. How many bacteria will there be after 2 hours?
b. How many bacteria will there be after 1 day?
4.
Does the table represent an exponential function? Explain.
5.
Does the rule
1
8
x
y
2
32
3
128
4
512
represent an exponential function? Explain.
Graph
Complete the table, then graph each function.
2. y 
1. y  2.5 x
x
y
-3
-2
-1
0
1
2
1 x
3
2
3. y  0.5(0.5) x
3
x
y
x
y
-3
-2
-1
0
1
2
-3
3
Growth and Decay
1. Tell whether the function represents exponential growth or exponential decay.
x
3
x
x
a. y  5.2  3
b. y  7  0.32
c. y  0.5 
2
-2
-1
0
1
2
3
Write and Evaluate Exponential Functions
1. An investment of $2000 doubles every 12 yr.
a. Model the value of the investment with an exponential function.
b. How much is the investment worth after 36 yr? After 60 yr?
2. Suppose you deposit $1000 in a savings account that pays 4.8% interest compounded monthly.
a. Write an exponential function to model the amount of money in your savings account.
b. How much will you have in your account after 1 yr? After 2 yr?
3. A population of 800 cheetahs decreases by 13% per year.
How many cheetahs will there be in the population after 5 years? Round your answer to the nearest
whole number.
4. Carbon-14 has a half-life of 5730 years and is used to date archaeological objects.
Fresh charcoal contains 13.60 grams of Carbon-14. Prehistoric cave paintings were found in Spain. A
piece of charcoal found in the ancient cave had 1.70 grams of carbon. From this information, determine
the age of the cave paintings.
Find the balance in the account.
5.
$3,300 principal earning 4%, compounded annually, after 3 years
6.
$1,600 principal earning 7%, compounded semi-annually, after 33 years
Homework
1. Reasoning Does the table below represent an exponential function? Explain why or why not.
Evaluate each function for x = –1, 1, 2.
3. y 
2. f (x) = 4 • 7x
4. f (x) = 13 • (1.3)
x
5.
2
3
6x
 4
h(x)  3g 
 5
x
6. The function y = 41 • 0.95x models the difference (in minutes) between men’s and women’s finishing times for the
Boston Marathon. The number of years since women first officially ran the race in 1972 is represented by x.
a. Does the exponential function represent growth or decay?
b. Estimate the difference between finishing times in 1990.
c.
Predict the difference between finishing times in 2015.
7. Find the balance in an account after 8 years if $500 is invested at 7% interest compounded annually.
8.
A tractor costs $15,450 and depreciates in value by 14% per year. How much will the tractor be worth after 3 years?