Some word problems for exponential functions

1) Someone invests $3080 in an account at 7% interest compounded annually. Let f(t) be the value (in dollars) of the account at t years after she has invested the $3080.

a)  Find an equation for f

b)  What is the base b of your model f(t) = a * b^t?

c)  What does it mean in this situation?

  1. The account balance does not change
  2. The account balance increases by 3080
  3. The account balance decreases by 7% per year
  4. The account balance increases by 7% per year

d)  What is the coefficient a of your model f(t) = a * b^t?

e)  What does it mean in this situation?

  1. The account balance decreases by 7% per year
  2. The final amount in the account after t years will be $3080.
  3. The account balance increases by 7% per year’
  4. The initial amount in the account was $3080

f)  What will be the account value in 10 years?

g)  Interpret in words the ordered pair (10, 6058.83)


2) Sales of portable MP3 players grew approximately exponentially from .07 billion dollars in 2002 to .84 billion dollars in 2004.

a) Predict the sales of MP3 players for the year 2007.

b) Predict the sales of MP3 players for the year 2007 if the growth had been linear instead of exponential.


3) The revenue from ring tones was $90 million in 2003 and has grown by about 122% per year since then. That is, each year the revenue is about 2.22 times the previous year’s revenue.

a)  Let r = h(t) be the revenue (in millions of dollars) from ring tones in the year that is t years since 2003. Find an equation of h.

b)  What is the r-intercept of the model?

c)  What does it mean in terms of the situation?

d)  What is the base b of the model?

e)  What does it mean in terms of the situation?

f)  Predict the revenue from ring tones in 2009?

g)  Research predicts that revenue from ring tones will be 879 million in 2009. If that happens, will each year’s revenue continue to be 2.22 times the revenue of the previous year? Yes or No?

b) Use the graph to answer:

What percent will be left after 20 years?

c) Use the graph to answer:

When will there be 12% of the radioactive element left in the tank?

d) Produce an exponential model for this situation

e) Use the model to answer:

What percentage of the element will remain in the tank after 80 years?

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