You bike 1 mile the first day of your training, 1.5 miles the second day, 2.5 miles the third day, and 4.5 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day?

32.5 miles on the 7th day

Step-by-step explanation:

1, 1.5, 2.5, 4.5

We need to determine the pattern

We are adding .5 + 1/4(2^n)

Lets check

n=1  .5+ 1/4(2) = .5+ .5 =1

n =2   .5 + 1/4*2^2 = .5 +1 = 1.5

n=3  .5 + 1/4 ( 2^3) = .5 + 8/4 = 2.5

n=4   .5 + 1/4 (2^4) = .5 + 16/4 = 4.5

n = 5  .5 + 1/4 (2^5) = .5 +32/4 = 8.5

n = 6   .5 + 1/4 (2^6) = .5 + 64/4 =16.5

n=7   .5 + 1/4(2^7)= .5 + 1/4(128) = 32.5

They bike 32.5 miles

Sketch the graph of y=7x

Reflect the graph across the y-axis to show the function y=7^-x

Stretch the graph vertically by a factor of 3 to show the function y=3x7^-x

Shift the graph up 2 units to show the function y=3x7^-x +2                        

Step-by-step explanation: