MA002
Unit 4 Assessment
Chapter 4: Exam A
1) Match the graphs with the equations.
y  log x
Letter ________
E
D
F
y  ln x
Letter _________
y  2x
Letter _________
y  3x
Letter _________
y  (0.4) x
Letter _________
y  ex
Letter _________
C
B
A
2) Fill in the following table:
Function
y-intercept
(0, 20)
Growth or
decay?
Decay
Growth or decay
rate
6% annual rate
(0, 5)
Growth
7% continuous rate
y  13(1.4) x
y  17e 0.35x
3) Granny wants to start a college account for her newborn granddaughter. How much
money does she need to deposit now into an account earning 3% compounded
quarterly so it will be worth $20,000 in 18 years?
_____________________
4) The population, P, of a group of rabbits t years after being released in a new habitat
t
is given by P(t )  500 1.03 .
a) How many rabbits were initially released?
________________________
b) Fill in the blank: The rabbit population is growing by _____% per year
c) How many rabbits will there be in 2 years?
__________________
d) When will there be 600 rabbits?
________________________
5) Solve the following equations for x.
a) 2log3  2 x  3  4
________________________
b) 3(4) x2  21
________________________
c) 4e12x  3  19
________________________
6) Find a formula for an exponential function such that f(1) = 3 and f(-1) = 12.
________________________
7) Rewrite this as a single logarithm: 2 log( x)  3 log( y)  log( z)
________________________
8) Solve for x in this equation: log( x  48)  log( x)  2
________________________
9) Bismuth-214 has a half-life of 20 minutes. What percent of the original amount is left
after one hour?
___________________
10) In 2003, there were 7225 Starbucks stores. In 2005, there were 10,241 Starbucks
stores. If Starbucks continues to increase exponentially at the same rate, find the
doubling time.
__________________
11) The Island of Niue is currently home to 5000 people, and the population has been
growing continuously by 8 %. The Cook Islands are currently home to 20,000
natives but the native population has been continuously decreasing by 6% each
year.
Write the equation for the population of the Island of Niue. N(t) = _______________
Write the equation for the population of the Cook Islands. C(t) = _______________
If these trends continue, during what year will the populations be the same?