Question

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

Answer 1

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)`