[cnycole]

This one is difficult to me because I'm not sure what the fixed rate is, or how to find it.

Question:

In 2005 the cost of a compact car averaged $15,500. In 2009, the cost of that model car averaged $17,250. Assume that th relationship between time and cost is linear.

Develop a formula for predicting the average cost of that model car in the future, in the form of C(x)=mx+b; x represents the number of years after 2005.


---> how do I find these values?

[jcaron2]

So C(x) in your formula is the cost as a function of time. The variable x is supposed to be the number of years since 2005. So the problem gives you two data points. One of them is (4, 17250). The 4 comes from the fact that 2009 is 4 years since 2005. Can you tell me what the other data point is?

Once you have two data points, the slope (a.k.a. the fixed rate), m, is easy to calculate. It's the change in C(x) over the change in x (delta cost/delta time). So what do you calculate for the slope m? That's how many dollars per year the cost increases.

Once you know the slope, you can calculate the y-intercept, b, by just writing out your whole equation (C = mx + b), plugging in either of your two known data points for C and x, along with the m you just calculated, and solving for b. So what do you get?

Once you know m and b, you have everything you need to write out your linear equation. So what's the answer?

[cnycole]

The other point is (0,15500)
The slope is 437.5
b=15500
C(x)=437.5x+15500
Is all this correct?

[jcaron2]

Yes. Well done!

[cnycole]

Yeaa! Thank you!