Transcript exponential function with base b

Exponential Functions
Name:______________
Date:_______________
Warm Up:
1. Find each valu e :
33 
24 
Solve for x : 3 x 1  27
2. Find each valu e : 41 
52 
2 x 3  16
42 
5 x-2  25
43 
40 
3. Negative exponents mean ________________________
Find each valu e : 4 -1 
4 -2 
4 -3 
4. The denominato r of a fractional exponents mean ________________________
1
Find each valu e : 4 2 
1
16 2 
1
64 3 
5. The numerator of a fractional exponents mean ________________________
3
Find each valu e : 4 2 
3
16 2 
2
64 3 
6. Complete the table for the function f(x) = 4x
x
-3
-2
-
-1

0
-
1

2
3
f(x)
Sketch a graph for the function f(x) = 4x

Discuss the domain and range f(x) =4x
y



















x



7. An exponential function with base b is a function with the formula:
f ( x)  ab x where a  0, b  1, and b  1
An exponential growth function has base b __________
An exponential decay function has base b ______________________
Which models below are growth models?
Which models below are decay models?
A. f ( x)  3(1.5) x
B. f ( x)  3(0.5) x
C. f (t )  3( 34 ) t
D. f ( x)  3( 13 ) x
E. f (t )  3( 43 ) t
8. Write a model for each problem.
A. Andy Graham has a savings certificate that is currently worth $10,500
and pays 6.5% interest compounded yearly.
B.
Scientists, Matos and Massarelli, were working on an experiment
which started with 10 bacteria. The bacteria doubled every hour.
C.
Bessy bought a gaming computer for $3,500.00. The value of her
computer will depreciate at the rate of 24% per year.
D.
The rural town for Mathville has been losing population at a rate of
5.8% per year. Its current population is 12,500.
9. Use your models to solve each problem.
A.
Andy Graham has a savings certificate that is currently worth
$10,500.00 and pays 6.5% interest compounded yearly.
What is the balance when the certificate matures in 5 years?
B. Scientists, Matos and Massarelli, were working on an experiment
which started with 10 bacteria. The bacteria doubled every hour.
Find the number of bacteria after 480 minutes.
C.
Bessy bought a gaming computer for $3,500.00. The value of her
computer
will depreciate at the rate of 24% per year. Estimate the value of the
computer in 3 years.
D. The rural town for Mathville has been losing population at a rate of 5.8%
per year for the last 10 years. Its current population is 12,500. What was its
population 10 years ago?