Page 218 - How To Solve Word Problems In Calculus

Chapter 8

Application to Business

and Economics

Rates of Change in Business
Many quantities in the business world are constantly chang-
ing. For example, your salary may increase if you stay with
the same company for many years or your debt may decrease
if you pay back your student loan.
It is useful to know how fast a quantity is changing.
After all, an employee whose salary changes by $10,000 over a
2-year time period is doing better than an employee whose
salary changes by the same amount over 5 years.
The derivative with respect to time measures how fast a
function is changing. This is known as the instantaneous rate
of change with respect to time. (See Chapter 2 for a discussion
of rates of change.)

EXAMPLE 1
t years after it was built, the property tax T on a small home
2
was T(t) = 15t + 35t + 2500 dollars. How fast did the pro-
perty tax increase 2 years after the home was built?

Solution

T (t) = 30t + 35

T (2) = 95
The tax increased at the rate of $95 per year.

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