### 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 e^{0.097t}

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

**SOLUTION:**

- t= 1996-1962 = 34. So C(34) = 1.35, or according to the model, a Hershey bar costs $1.35 now.
- t = 2000 -1962 = 38. C(38)= 1.99. According the model, a Hershey bar will cost $1.99 in the year 2000.
- C=5; we use this in the formula and solve for t. 5 = 0.05 e
^{0.097t}

100 = e^{0.097t}

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.

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