Question

2. In 2020 the depth of Lake Michigan was 900 feet. Back in the year 2010 the depth of the wa

was 1000 feet. The depth of the water is decreasing by a certain percentage each year.
(a) Find a function, d(t) that gives the depth of the water t years after the year 2000.
In the formula d(t) = ab' ,round b to 4 decimal places and a to the nearest whole num
20

Answer 1

Explanation:

Ten year span t = 10

1000 ( b)^t = 900

(b)^10 = 900/ 1000

b = .9895

so the formula becomes d(t) = 1000(.9895)^t

where t is the number of years since 2010

BUT your question asks 'since 2000'

find depth in year 2000: ( ten years later the depth is 1000 )

1000 = a (.9895)^10

1111 = a this is the depth in 2000

NOW the formula becomes d(t) = 1111(.9895)^t

where t is the number of years since 2000