Question

Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.

f ( t ) = 1,200 times (1.05)^t

Which of the following statements are true for the function given?

The independent variable is f(t).

When f(2) = 1,233, the 2 represents "the year 2002," and the 1,233 represents "1,233 tons of garbage produced."

The independent variable is t.

The dependent variable is f(t).

The dependent variable is t.

When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."

When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."

Answer 1

The following statements in this case are correct:
1) The independent variable is t.
2) The dependent variable is f (t).
3) When f (2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
4) When f (4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."

Note: for statements 3) and 4) the following is done:
f (2) = (1200) * (1.05) ^ 2 = 1323
f (4) = (1200) * (1.05) ^ 4 = 1458.6