Question

A report by the US Geological Survey indicates that glaciers in Glacier National Park, Montana, are shrinking. Recent estimates indicate the area covered by glaciers has decreased from over 25.5 km2 in 1850 to about 16.51 km2 in 1995. Let A=f(t) give the area (in square km) t years after 2000, and assume f(t)=16.2−0.062t.a. Find and explain the meaning of the slope. Which statement best explains its significance? A. The total area covered by glaciers is increasing by 0.062 km2 every year B. The total area covered by glaciers decreased by 16.2 km2 from 1850 to 2000 C. The area covered by glaciers is decreasing by 62,000 m2 every year. D. The area covered by glaciers is decreasing by 16.2 km every year E. The area covered by glaciers is decreasing by 62 m every year F. None of the aboveb. Find and explain the meaning of the A-intercept. Which statement best explains its significance? A. The total area covered by glaciers will decrease by 0.062 km from 2000 to 2001. B. The area covered by glaciers in 2000 was 16.2 km^2 C. The total area covered by glaciers decreased by 16.2 km2 from 1850 to 2000 D. The area covered by glaciers in 2000 was 0.062 km E. The area covered by glaciers is decreasing by 16.2 km2 every year F. None of the above.c. For both expressions listed below, enterthe letter A-E of the statement which best explains their practical meaning. There are extra, unused statements.1. ____________: f(t)= 12 then t is2. ____________: f(12) isA. How much area wi be covered by glaciers in 12 years B. The number of years after 2000 that the amount of glacier area that has disappeared is 12km^2 C. The number of years after 2000 that the total area covered by glaciers will be 12 km D. The amount of glacier area that disappears in 12 years. E. How much area will be covered by glaciers in 2012.d. Evaluate f(12):________e. How much glacier area disappears in 12 years?f. Solve f(t) =12 .t = _________-(round your answer to one decimal place)

Answer 1

a) C

b) B

c) C, E

d) 15.5

e) 0.7

f) 67.7

Explanation

a) A linear equation can be written as
`y=mx+c` where
`m` is the slope and
`c` is the intercept on the
`y`-axis. The slope describes how
`y` changes when
`x` changes. A negative value means the it is a decreasing change. In our case,
`y` is
`A` and
`x` is
`t`. Thus, the slope of the equation is
`m=-0.062`. This means that the area of glacier is decreasing by
`0.062 \text{km}{}^2 = 62000 \text{m}{}^2` every year since 2000.

b) The
`A`-intercept (= 16.2
`\text{km}{}^2`) represents the area covered when
`t=0`. But
`t=0` starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2
`\text{km}{}^2`.

c)
`A=f(t)` means the area covered after year 2000. Setting it to 12 means the area covered after
`t` years is 12
`\text{km}{}^2`).
`t` is therefore the number of years since 2000 that the total area covered will be 12
`\text{km}{}^2`).

d)
`f(12)=16.2−0.062*12 =16.2-0.744 = =15.456 15.5 \text{km}{}^2` to 1 decimal place.

e) The term involving
`t` represents the disappearing area. In 12 years, the disappeared area is
`0.062*12=0.744 =0.7 \text{km}{}^2` to 1 decimal place.

f)
`f(t)=16.2−0.062t =12`

`0.062t = 16.2-12 = 4.2`

`t = (4.2)/(0.062)=67.7419\ldots =67.7` years to 1 decimal place.