Suppose your annual income is I ( t ) = 64,000 + 2,000 t (0 ? t ? 3) dollars per

Question

Suppose your annual income is

I(t) = 64,000 + 2,000t   (0 ? t ? 3)

dollars per year, where t represents the number of years since you began your job, while your annual expenses are

E(t) = 54,000 + 1,500t   (0 ? t ? 3)

dollars per year. Find the area between the graphs of I(t) and E(t) for 0 ? t ? 3.
$  

What does your answer represent?

your average savings per yearyour average expenses per year    your average income per yearthe total amount you were able to save over the first three yearsthe total amount you spent over the first three yearsthe total amount you earned over the first three years

Explanation / Answer

top - bottom as the following:

3
? (64,000 + 2,000t) - (54,000 + 1,500t)
0

3
? (64,000 + 2,000t - 54,000 - 1,500t)
0

3
? (10,000 + 500t)
0

. . . . . . . . . . . . . . . . . . .3
(10,000 * t + (500/2) * t^2) ]
. . . . . . . . . . . . .. . . . . .0

(10,000 * (3 - 0) + 250 * (3^2 - 0^2)

30,000 + 250 * (9) = 32250 unit^2

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