A glacier covered about 130 acres in 2003 and was shrinking at a rate of about 4.8% per year.
(a) Write a formula for the size, S, of the glacier, in acres, as a function of years t since 2003.
b) Use the model to predict the size of the glacier in the year 2009.
c) According to the model, how many acres of ice were lost from the glacier between 2003 and 2008?
this is just another exponential function.
S = 130(1+0.048)^t
See your first post below
but shrinking not growing - use - sign
S = 130(1-0.048)^t
(a) To find a formula for the size of the glacier, we need to start with the initial size of the glacier in 2003 and then incorporate the rate at which it is shrinking each year.
Let S represent the size of the glacier in acres, and t represent the number of years since 2003.
Since the glacier is shrinking at a rate of 4.8% per year, we can express this as a decimal by dividing 4.8 by 100, which gives us 0.048.
To find the size of the glacier in acres at any given year, we can use the formula:
S(t) = Initial Size - (Rate of Shrinkage * Initial Size)
From the information given, we know that the initial size is 130 acres, so the formula becomes:
S(t) = 130 - (0.048 * 130)
Simplifying this equation:
S(t) = 130 - 6.24t
Therefore, the formula for the size of the glacier, S, as a function of years t since 2003 is:
S(t) = 130 - 6.24t
(b) To predict the size of the glacier in the year 2009, we need to substitute t = 6 (since 2009 is 6 years after 2003) into the formula we derived in part (a):
S(6) = 130 - 6.24 * 6
Simplifying this equation:
S(6) = 130 - 37.44
S(6) ≈ 92.56
Therefore, the predicted size of the glacier in the year 2009 is approximately 92.56 acres.
(c) To find the number of acres of ice lost from the glacier between 2003 and 2008, we can find the size of the glacier in 2008 (t = 5) and subtract it from the initial size in 2003.
Using the formula derived in part (a):
S(5) = 130 - 6.24 * 5
Simplifying this equation:
S(5) = 130 - 31.2
S(5) = 98.8
Therefore, the size of the glacier in 2008 is approximately 98.8 acres.
To find the number of acres lost, we subtract the size in 2008 from the initial size in 2003:
130 - 98.8 = 31.2
According to the model, approximately 31.2 acres of ice were lost from the glacier between 2003 and 2008.