Question

. The Federal Helium Reserve held about 16 billion

cubic feet of helium in 2010 and is being depleted by
about 2.1 billion cubic feet each year.

a. Give a linear equation for the remaining federal
helium reserves, R, in terms of t, the number of
years since 2010.
b. In 2015, what will the helium reserves be?
c. If the rate of depletion doesn’t change, in what year
will the Federal Helium Reserve be deplete

Answer 1

Explanation:

a. Since the Federal Helium Reserve is being depleted by 2.1 billion cubic feet each year, we can write a linear equation for the remaining federal helium reserves R in terms of t, the number of years since 2010, as:

R = 16 - 2.1t

b. To find the helium reserves in 2015, we need to substitute t = 5 in the equation we found in part a:

R = 16 - 2.1t

R = 16 - 2.1(5)

R = 16 - 10.5

R = 5.5

Therefore, in 2015, the helium reserves will be 5.5 billion cubic feet.

c. To find the year when the Federal Helium Reserve will be depleted, we need to solve for t when R = 0 in the equation we found in part a:

R = 16 - 2.1t

0 = 16 - 2.1t

2.1t = 16

t = 16 / 2.1

t ≈ 7.62

Therefore, if the rate of depletion doesn't change, the Federal Helium Reserve will be depleted in about 7.62 years from 2010, which corresponds to the year 2018.