Download Mixed Practice Homework Exponential Equations

Mixed Practice Homework – Exponential Equations and Logs
Name:
1. A petri dish has 100,000 bacteria. The population is decreasing at a rate of 16% per day.
a) Write a (non-continuous) exponential model that tells us the population (y) at x days.
b) Use this model to predict the number of bacteria in the petri dish after 20 days.
c) About how many days would it take before there were only 100 bacteria left in the petri dish?
2. Suppose you invest $6000 at an annual interest rate of 2.5%, compounded continuously.
a) Write an equation that would tell you the amount of money you would have after x years.
b) How much money would you have after 50 years?
c) About how many years would it take for you to have at least $10,000 in the account?
3. Solve the following exponential equations by using like bases.
x
a) Solve for x:
8 x  4 x 1
b) Solve for x:
1
x2
   27
9
4. Rewrite each expression in logarithmic form.
a)
63  216
b)
e0  1
c)
7 2  49
log 1000  3
c)
ln 1  0
5. Rewrite each expression in exponential form.
a)
log 5 25  2
b)
6. Solve each logarithmic equation below. Where appropriate, round to the nearest ten-thousandth.
a)
b)
log( x  2)  log( 3x)  1
2 log 3 x  log 3 25
b)
ln( x  2)  3
c)
ln( x  2)  ln( 6)  ln( 5 x  1)
7. Solve each exponential equation using logarithms. Round answers to the nearest ten-thousandth.
x
a)
2 x  21
b)
1
   60
5
c)
3 x  5  17
d)
2(6) x  400