519,782 views
7 votes
7 votes
A mountain in Jackson County is eroding and losing elevation at a rate of 5% every

millennium. If the current elevation is 1,300 meters, how tall will the mountain be in 8
millennia?
mund your anuor to the noroctwhold number

User Xjfengck
by
2.5k points

1 Answer

12 votes
12 votes

Answer:

862 m (nearest whole number)

Explanation:

General form of an exponential function:
\sf y=ab^x

where:

  • a is the y-intercept (or initial value)
  • b is the base (or growth factor)
  • x is the independent variable
  • y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

If the mountain is losing elevation at a rate of 5% every millennium , then it as every millennium passes, it will be 95% of the height it was in the previous millennium (as 100% - 5% = 95%)

Given:

  • a (initial value) = 1300 m
  • b = 95% = 0.95
  • x = 8 millennia

Substituting these values into the formula:


\sf \implies y=1300(0.95)^8


\sf \implies y=862.4467607...


\sf \implies y=862 \ m \ (nearest \ whole \ number)

User Adan
by
3.1k points