Help find average rate of change

Problem 2

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Explanation:

When we have an interval [a,b], the average rate of change over this interval is given by the formula

You probably can notice that we have something that looks eerily similar to the slope formula. That's because average rates of change are basically the same as the slope of the straight line through the endpoints of the interval. The f(b)-f(a) is the change in y of f(x) outputs. The b-a down below is the change of x values when going from x = a to x = b.

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Let's evaluate the function at x = 1

f(x) = x^2+1

f(1) = 1^2+1

f(1) = 2

Repeat for x = 3

f(x) = x^2+1

f(3) = 3^2+1

f(3) = 10

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We have enough info to evaluate the original formula I mentioned earlier

The average rate of change on this interval is 4

This is the same as saying the slope of the line through (1,2) and (3,10) is m = 4

See the graph below.

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~

answer: 1inch=7days  

12inch=12*7=84days

step-by-step explanation: