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The floor of a canyon has an elevation of −14.5feet. Erosion causes the elevation to change by −1.5 feet per year. How many years will it take for the canyon floor to have an elevation of −31

Verified Answer :

11 years 

work:

-31-14.5=-16.5

16.5/1.5= 11

11 is the answer

carlosego

For this case, the first thing we must do is define variables.

We have then:

x: number of years

y: elevation in feet

Then, we write the equation that models the problem.

We have then:

\(y = -1.5x - 14.5
\)

Then. for an elevation of -31 feet we have:

\(-31 = -1.5x - 14.5
\)

From here, we clear the number of years.

We have then:

\(-1.5x = -31 + 14.5

-1.5x = -16.5
\)

\(x = \frac{-16.5}{-1.5}

x = 11
\)

Answer:

It will take for the floor to have an elevation of -31 about 11 years.

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