The dollar value of a scooter is a function of the number of years, t, since the scooter was purchased.

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The function f is defined by the equation f(t) = 3500.\frac{1}{2}^{t}. What is the best choice of domain for the function f?

  1. -10 \leq t \leq 10
  2. -10 \leq t \leq 0
  3. 0 \leq t \leq 10
  4. 0 \leq t \leq 100

Sangeetha Pulapaka

The domain of a function is all the values on the x-axis. The values on the x-axis are independent variables. The number of years lies on the x-axis and the dollar value of the scooter lies on the y-axis. Since the number of years start can only start from 0 and cannot be a negative number, choices 1 and 2 can be eliminated.

f(100) = 3500.\frac{1}{2}^{100} will result in a large number with a very high exponent.So,the number of years cannot be a maximum of 100 since the dollar value cannot be a large number with a very high exponent.

So, we are left with choice 4, When t = 10, f(10) = 3500.\frac{1}{2}^{10}

f(10) = \frac{3500}{1024} \approx 3.42 dollars.

Skills to recall:

What is the domain of a function


What is an exponential function


How to find 2^{100}