To restore a depleted wetland, conservationists pump water into a basin. The volume of wat… — SAT

To restore a depleted wetland, conservationists pump water into a basin. The volume of water in the basin, $W$ , in thousands of gallons, $t$ hours after the pumping begins is modeled by the equation $W = 12.5t + 85$ . According to the model, how many hours of pumping are required for the volume of water in the basin to increase by $150$ thousand gallons?

Cevap: 12 hours

Cevap

The linear equation is given in slope-intercept form,

W = mt + b

, where

m = 12.5

is the slope and

b = 85

is the y-intercept. In this context, the slope

m = 12.5

represents the rate at which water is pumped into the basin, which is

12.5

thousand gallons per hour. To find the number of hours required for the volume of water to increase by

150

thousand gallons, divide the total increase by the rate:

\frac{150}{12.5} = 12

hours.

Adım Adım Çözüm

Identify the rate of water volume increase per hour from the equation.

The rate is

12.5

thousand gallons per hour.

In the linear equation

W = 12.5t + 85

, the coefficient of

t

(the slope) represents the rate of change of the water volume with respect to time.

Set up a relation to find the time

t

for a volume increase of

150

thousand gallons.

12.5t = 150

The change in volume is equal to the rate of change multiplied by the time elapsed.

Solve the equation for

t

t = 12

Dividing both sides of the equation

12.5t = 150

12.5

isolates

t

Anahtar Kavram

Interpreting the slope of a linear equation in context as a rate of change.

Tahmini Süre:1m 30s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru