Luis has saved $6. he doubles the amount he saves each week. does this represent an exponential function? complete:

represent an exponential function , because his savings increase by a

you so much in advanced

This represent an exponential function, because his savings increase by a constant factor of 2.

Step-by-step explanation:

It is given that,

Luis has saved $6 and he doubles the amount each week.

So, the amount saved in the next week = 6×2 = 12

This gives the amount saved in the third week = 12×2 = 24

So, we get the sequence 6, 12, 24, 48,.....

It can be written as, 6×2⁰, 6×2¹, 6×2², 6×2³,.....

So, the sequence in the exponential form , where 'n' is a natural number.

Also, 6, 12, 24, 48,.....

The numbers are increasing by the factor =

Hence, we get,

This represent an exponential function, because his savings increase by a constant factor of 2.

60%

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240