Joel is training for a marathon. Right now he can run 3 miles. In two weeks he plans on running 5 miles, in four weeks he plans on running 8 miles.

If Joel's mileage continues growing with the same pattern, how many miles will he be running in 10 weeks?

A) 15
B) 17
C) 23
D) 26

c) 23

Step-by-step explanation:

The relationship between the amount of growth per 3 weeks is proportional.

If you made a table it would look similar to:

x      |          y  | Rate of Change

1      |          3  | +0

2     |          5  | +2

4     |          8  | +3

6     |         12  | +4

8     |          17 | +5

10    |         23 | +6

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.