INTRODUCTORY EXERCISES-Logarithms and Modelling


(1) The cost of a Hershey chocolate bar in 1962 was 5 cents. The exponential function describing the growth of the cost of the chocolate bar is given by:

C(t) = 0.05 e0.097t

  1. What is the cost of the Hershey Bar now?
  2. What is the cost in the year 2000?
  3. According to this model, when will the Hershey Bar cost $5.00?

SOLUTION:

  1. t= 1996-1962 = 34. So C(34) = 1.35, or according to the model, a Hershey bar costs $1.35 now.
  2. t = 2000 -1962 = 38. C(38)= 1.99. According the model, a Hershey bar will cost $1.99 in the year 2000.
  3. C=5; we use this in the formula and solve for t. 5 = 0.05 e0.097t
    100 = e0.097t
    ln(100) = 0.097t or t = (ln 100)/0.097 = 47.48.

    The Hershey bar will cost $5.00 in about 48 years, or around the year 2010.


Click Here To Return To The Introductory Exercises.

Click Here To Return To The Main Menu.