Download Algebra 2B Word Problems Chapter 6 1. The size of a certain insect

Algebra 2B
Word Problems Chapter 6
1. The size P of a certain insect population at time t (in days) obeys the function P  t   500e0.02t .
a) Determine the number of insects at t  0 days.
b) What is the growth rate of the insect population?
c) What is the population after 10 days?
d) When will the insect population reach 800?
e) When will the insect population double?
f) Graph the function.
2. Strontium 90 is a radioactive material that decays according to the function A  t   A0e0.0244t , where
A0 is the initial amount present and A is the amount present at time t (in years). Assume that a
scientist has a sample of 500 grams of strontium 90.
a) What is the decay rate of strontium 90?
b) How much strontium 90 is left after 10 days?
c) When will 400 grams of strontium 90 be left?
d) What is the half-life of strontium 90?
e) Graph the function.
3. The population of a midwestern city follows the exponential law. If the population decreased from
900,000 to 800,000 from 2003 to 2005, what will the population be in 2007?
4. A culture of bacteria obeys the law of uninhabited growth. If 500 bacteria are present initially and
there are 800 after 1 hour, how many will be present in the culture after 5 hours? How long is it until
there are 20,000 bacteria?
5. A number of bacteria present in a culture at time t=0(in hours) is 1000. After 5 hours the number of bacteria increase
to 1050. The number of bacteria obeys the law of uninhibited growth.
a) What is the growth rate of the bacteria?
b) Write an equation that models this situation.
c) What is the population after 8 hours?
d) When will the number of bacteria reach 1700?
e) When will the number of bacteria double? Use the right term to describe this situation.
6. The half-life of radioactive cobalt is 5.27 years. There are 100 grams of it present in the sample now.
a) Write an equation that models this situation.
b) How much of it will be present in 20 years?
c) When will 10 grams of radioactive cobalt be left?
7. The half-life of radium is 1690 years. There are 10 grams of it present in the sample now. How much of it will be
present in 50 years? In 1000 years? Draw the graph of the function describing this situation.
8. If $1550 is invested in an account which earns 9% interest compounded annually, what will be the balance of the
account at the end of 4 years? 10 years?
9. The population of a town in Arizona was 27,480 in 1985 and 34,895 in 1995. Model this situation using the
appropriate exponential equation. Predict the population in 2020.