Question

Suppose that an office chair costs $50 in 2017, and $52.90 in 2018 . Office chairs continue increasing in price, but this price increase decreases by 10 cents each subsequent year. Use anti-derivatives to express the price of a chair as a function of t, where t represents the number of years that have passed since 2017,50 that t=0 corresponds to the year 2017,t=1 corresponds to the year 2018 , and so on.

Answer 1

To express the price of the chair as a function of time, we use the equation P(t) = $50 + $(2.90 - 0.10t), where P(t) represents the price of the chair after t years since 2017.

Step-by-step explanation:

To express the price of the chair as a function of time, we need to find the equation that represents the price increase. We know that the price increase decreases by 10 cents each subsequent year. Since the price in 2017 is $50 and the price in 2018 is $52.90, we can find the equation for the price increase as follows:

Let P(t) be the price of the chair after t years since 2017. We have P(0) = $50 and P(1) = $52.90. The price increase is $52.90 - $50 = $2.90. Since the price increase decreases by 10 cents each subsequent year, we can express the price increase as $(2.90 - 0.10t). Therefore, the equation for the price of the chair as a function of t is P(t) = $50 + $(2.90 - 0.10t).