Due to rising global temperatures, the thickness T, in meters, of a mountain glacier is de… — SAT

Due to rising global temperatures, the thickness $T$ , in meters, of a mountain glacier is decreasing at a constant rate. A researcher models the thickness of the glacier using the equation $T = 48.5 - 0.12w$ , where $w$ represents the number of weeks since the start of a monitoring study. According to the model, by how many meters does the thickness of the glacier decrease every $50$ weeks?

Cevap: 6 meters

Cevap

The glacier's thickness decreases by 6 meters.

In the linear model

T = 48.5 - 0.12w

, the thickness

T

decreases by

0.12

meters for each increase of

1

w

(each week). Therefore, over a period of

50

weeks, the total decrease in thickness is

0.12 \times 50 = 6

meters.

Adım Adım Çözüm

Identify the weekly rate of decrease from the slope of the equation.

0.12 meters per week

In the linear model

T = 48.5 - 0.12w

, the coefficient of

w

-0.12

. This slope represents the rate of change, indicating a decrease of

0.12

meters in thickness per week.

Calculate the cumulative decrease over 50 weeks.

Multiply the weekly rate of decrease (

0.12

meters per week) by the duration (

50

weeks) to obtain the total decrease:

0.12 \times 50 = 6

Anahtar Kavram

Interpreting the slope of a linear relationship in context

Tahmini Süre:1m 30s

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