Question

A mountain has an elevation of 19,293 feet. In 1901, the glacier on this peak covered 4 acres. By 2005 this glacier had melted to only 1 acre.

A) Assume that this glacier melted at a constant rate each year. Find this yearly rate.

B) Use your answer from (A) to write a linear equation that gives the acreage A of this glacier t years past 1901.

Answer 1

The melting of the glacier can fit really nicely onto an exponential decay function of the form: q=Q*e^(-kt) where q=amount remaining, Q=initial amount, e=exponential, k=melting rate, t=time in years. Note that we use -k because the amount of ice is reducing.
So from the problem, Q=4 acres, q=1 acre, e=value in calculator of course, t=(2005-1901)=104 years.
Plug those into the equation,
1=4*e^(-104k)
Now solve for k to get the constant rate of melting. I hope that helps.

Answer 2

so what about B?

Answer 3

i'm still kind of lost

Answer 4

Alright. Have you learnt about exponential functions?

Answer 5

A little

Answer 6

I have applied the that knowledge here. Exponential functions have the form:
Q=Q(1)*e^(-kt)
Where Q is the quantity being studied, and Q(1) is the initial amount of the quantity, e is the exponential(value given in calculator), and k is the constant of decay or growth (in this case decay because it is negative, and t is the time elapsed.
Does this sound familiar?

Answer 7

no not at all! uggghhhh

Answer 8

Alright. We can still do this. Which math class are you taking, so that I know which methodology to explain with.

Answer 9

university of phoenix mat/116

Answer 10

Alright. Which category does that fall into? Calculus or Algebra?

Answer 11

algebra

Answer 12

No prob. You'll get this really fast. Just a sec...

Answer 13

Now, imagine that we have a certain car whose value decreases by 5% each month. If its initial value 2 months ago was $1000, 1 month ago its value was 95% of 1000=950,
last month its value was 95% of 950 = 902.5, this month its value is 95% of 902.5=857.375.
Notice the trend: 1000,950,902.5,857.375.
This trend fits into the equation: value=initial value*percentage remaining^time
e.g. value now = 1000*.95^3 =857.375
From this case scenario, we can derive the formula:
amount=initial amount*percentage remaining^time.
Can you use this formula to solve the question now?

Answer 14

i'll try if not I'll just skip it

Answer 15

thanks

Answer 16

You're welcome.