Question

When most American’s throw away their laundry detergent bottle it has about 12 of an ounce of detergent left in it. If you use Dexter's equation y=-1.6x+50 and Mya’s equation for her laundry detergent, which is y=50(.75)^{x} who will throw away their laundry detergent bottle first?

A . Dexter and it will take about 31 loads of laundry

B. Mya and it will take about 16 loads of laundry

C. Dexter and it will take about 50 loads of laundry

D. Mya and it will take about 22 loads of laundry

Answer 1

The correct option is;

B. Mya and it will take about 16 loads of laundry

Explanation:

The given parameters are;

The amount of laundry detergent left the bottle when throwing away a detergent bottle = 1/2 of an ounce

Dexter's equation for his laundry is y = -1.6·x + 50

Mya's equation for her laundry is y = 50 × 0.75ˣ

Where x represents the loads of laundry, and y represent the amount laundry detergent left in the bottle

The assumption is made that the laundry rate of Dexter and Mya are equal

For Dexter, we have;

1/2 = -1.6·x + 50

1.6·x = 50 - 1/2 = 49.5

x = 49.5/1.6 = 30.9375 ≈ 31 loads of laundry

For Mya, we have;

1/2 = 50 × 0.75ˣ

1/100 = 0.75ˣ

0.75ˣ = 1/100

log(0.75ˣ) = log(1/100)

x·log(0.75) = log(1/100)

x = log(1/100)/(log(0.75)) ≈ 16 loads

Therefore, Mya will throw away her detergent bottle first, after 16 loads of laundry