Exponential Eq

[KLS2111]

I have the problem:

The cost at the surface is 15$ and $30 at 50 feet, write the exponential equation expressing price per foot in terms of depth. y=ab^x

I know that depth is x.. but I am confused what a and b symbolize.

Would b be price per foot? so like 30/50? I think I could do the problem if I know what a and b are supposed to stand for.

 

[galactus]

I suppose they want something like this.

when x=0, we are at the surface and the cost is y=$15.

when x=50, we are 50 feet down and the cost is y=30.

\(\displaystyle \L\\15=ab^{0}\Rightarrow{a=15}\)

\(\displaystyle \L\\30=15b^{50}\Rightarrow{b=2^{\frac{1}{50}}}\)

\(\displaystyle \L\\y=15(2^{\frac{1}{50}})^{x}\)

 

[stapel]

The cost at the surface is 15$ and $30 at 50 feet, write the exponential equation expressing price per foot in terms of depth.

That's the entire exercise...? They don't define what the cost is for (piping? fencing?), what the surface is on (a ship's deck? a mine entrance?), or what the depth is into (the bowels of the ship? the mine shaft?)...? How frustrating for you!

You might want to ask your instructor for clarification.

Eliz.