Question

The function that represents bruce’s elevation in feet over time in hours is an exponential function that starts at 1,505 feet. The first hour, his elevation change is six feet. Each successive hour, his average elevation change for the hike becomes six times the previous hourly elevation change. Write a function for Bruce’s elevation. Is it an exponential growth or an exponential decay function?

Answer 1

The function for Bruce’s elevation is
`f(x)=1505(6)^x` and because b=6 that is greater than 0, it is an exponential growth function.

Explanation:

We have given initial Bruce’s elevation = 1,505 feet.

We know, the exponential function
`f(x)=a(b)^x`, where a is the initial value, b is the growth factor and x is the exponent represents time in hours.

Each successive hour, his average elevation change for the hike becomes 6 times the previous hourly elevation change.

Therefore, initial value a=1505, growth factor b for exponential function
`f(x)=a(b)^x` is 6.

Now we can plug a=1505 and b=6 in
`f(x)=a(b)^x` , we get

`f(x)=1505(6)^x`

Also note, if b>0, it would be an exponential growth function.

Therefore, the function for Bruce’s elevation is
`f(x)=1505(6)^x` and because b=6 that is greater than 0, it is an exponential growth function.