Thread: explorations

A companys profit for 2000 was 5 million. Each year, the profit increases by 2 million. Let p=f(t) represent the profit(in million of dollars) for the year that is t years after 2000.
1. Find an equation for f. Write the equation using f(t) notation. Also, write the equation in terms of p and t.
2. Use the equation for f to predict when the company will have a profit of 21 million.
3. In problem 1 you found the equation p=2t+5. Solve this equation for t.
4. Substitute 21 for p in your equation from problem 3 and solve for t
5. Compare your results for problems 2 and 4
6. Enter the equation you found in problem 3 in graphing calc to help complete the table:
Profit Years
21 t
22
23
24
25
7. In problems 2 and 4 you used two different methods for finding when the company will have a profit of 21 million. If the company wants to know when it might attain 15 different profit levels, which method would be the best to use?

Originally Posted by getnaphd

A companys profit for 2000 was 5 million. Each year, the profit increases by 2 million. Let p=f(t) represent the profit(in million of dollars) for the year that is t years after 2000.
1. Find an equation for f. Write the equation using f(t) notation. Also, write the equation in terms of p and t.
2. Use the equation for f to predict when the company will have a profit of 21 million.
3. In problem 1 you found the equation p=2t+5. Solve this equation for t.
4. Substitute 21 for p in your equation from problem 3 and solve for t
5. Compare your results for problems 2 and 4
6. Enter the equation you found in problem 3 in graphing calc to help complete the table:
Profit Years
21 t
22
23
24
25
7. In problems 2 and 4 you used two different methods for finding when the company will have a profit of 21 million. If the company wants to know when it might attain 15 different profit levels, which method would be the best to use?

Exactly what are the difficulties you are having with this?

RonL

I don't even know where to begin. I have no idea how to do an equation with a notation.

Originally Posted by getnaphd

A companys profit for 2000 was 5 million. Each year, the profit increases by 2 million. Let p=f(t) represent the profit(in million of dollars) for the year that is t years after 2000.
1. Find an equation for f. Write the equation using f(t) notation. Also, write the equation in terms of p and t.

This means write the profit n years after 2000 in the form of an equation



Now compute a few years profit from what you are told:






Plot these an some graph paper (or in Excel) and you will see that they fall on a straight line.

You should know that the equation of a straight line takes the form:



So using the calculated values we can find and .

As we have , and as , we also have , so the required line is:



RonL

Originally Posted by getnaphd

A companys profit for 2000 was 5 million. Each year, the profit increases by 2 million. Let p=f(t) represent the profit(in million of dollars) for the year that is t years after 2000.
1. Find an equation for f. Write the equation using f(t) notation. Also, write the equation in terms of p and t.

CaptainBlack did an excellent job. Here's another way to think about it.

when t = 0 we have:

p(0) = 5 .........since we start with 5 million

after every year, we increase our profits by 2 mill, so when t = 1 we have:

p(1) = 5 + 2 (note, there is 1 2 when we have 1 year)

when t = 2

p(2) = 5 + 2 + 2 (note, there are two 2's when we have 2 years)

when t = 3

p(3) = 5 + 2 + 2 + 2 (note we have three 2's when we have 3 years)

so obviously there is a pattern. we make 2 mill with each passing year, so for t years we simply multiply t by 2 to find how much profit we gained since 2000.

thus, p(t) = 5 + 2t .............that is we add 2 million per year, so after t years we would have added 2t million

For part 2. Use the equation for f to predict when the company will have a profit of 21 million?

Do I just substitute 21 for f(t)?

Originally Posted by getnaphd

For part 2. Use the equation for f to predict when the company will have a profit of 21 million?

Do I just substitute 21 for f(t)?

yes, and solve for t