Question

5.
In 1930, the record for the 400-m run was 46.8 sec. In 1970, it was 43.8 sec. Let R(t) = the record in the 400-m run and t = the number of years since 1930.
a. Find a linear function that fits the data. ( b. Use the function of part (a) to estimate the record
i. in 2003 ii. in 2006.
c. When will the record be 40 sec?
In 1982, 1250 students attended Westside College. By 1997, the college had 1425 students. Let c(t) represent the number of students at the college t years after 1982.
a. Find the linear function that fits the data. ( )
b. Use the function from part (a) to predict the num

Answer 1

Okay, you're trying to fit a straight line to the known data. 1930 is t = 0, and R(0) = 46.8. R(1970-1930) = R(40) = 43.8. Think of t as x, and R(t) as y. Use the two known points to find the slope of the line, and the slope-point formula to find the equation for the line.

Having done that, use the equation to find the desired values. Don't forget that your equation takes the number of years since 1930 as its argument, not the actual year.

Answer 2

I am still slightly confused! I totally understand the points, but I am not sure how to plug in the numbers to get the answer? Does that make sense?

Answer 3

Okay, here's your data:

x y
0 46.8
40 43.8

Find the slope:
\[m = \frac{y_2 - y_1}{x_2-x_1}\]Write an equation with that slope through a known point:\[y-y_0 = m(x-x_0)\]