Question

you collect a basketball that's worth $150. Each following year it doubles in worth from the previous year. Write a function that shows the worth,w(t), at any given time,t.

Answer 1

150(2)^t

Explanation:

The function that represents the worth, w(t), of the basketball at any given time, t, can be written as:

w(t) = 150(2)^t

where t is the number of years since the basketball was collected.

This function uses the formula for exponential growth, where the value of the basketball doubles each year. The initial value of the basketball is $150, and the value is multiplied by 2 for each year that passes. Therefore, after one year, the basketball is worth $300 (2 times $150), after two years it is worth $600 (2 times $300), and so on.

By plugging in different values of t, we can calculate the worth of the basketball at any given time.