Question

the percentage P of smokers who are still smoking t years after starting can be resredented by the equation p= - 2.5t+60A) find the coordinates for the t intercept B) what are the units for each coordinate of the t interceptC) write a sentence interpreting the t intercept in terms of the information given in the problem

Answer 1

We are given the following equation:

`p=-2.5t+60`

In this case, "p" represents the percentage of smokers, and "t" represents time in years. Part A. We are asked to determine the t-intercept of the equation. To do that we will set the equation to zero and solve for "t".

Setting the equation to zero:

`-2.5t+60=0`

Now, to solve for "t" we will subtract 60 from both sides:

`\begin{gathered} -2.5t+60-60=-60 \\ -2.5t=-60 \end{gathered}`

Now we will divide both sides by -2.5:

`t=-(60)/(-2.5)`

Solving the operations:

`t=24`

therefore, the t-intercept is 24 years.

The coordinate for the t-intercept is then:

`(t,h)=(24,0)`

Part B. The units of the time coordinate are years and the p-coordinate is a percentage.

Part C. The t-intercept represents the time when the percentage of smokers is zero. It can be interpreted that 24 years is the maximum time where one can find smokers that are still smoking since at this time the percentage reduces to zero.