"solve the problem of exponential growth. according to the u. s. census bureau, the population of the united states in 2010 was 308 million. this is a 9.6% increase over the 2000 count. assuming this continued what would the population be in 2030? "

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

(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