Exponential equations and table of values

[Rumor]

I wasn't exactly sure where this fits in, but..

I'm given these values:

x: 0,2,4,6,
y: 2.000,3.000,4.500,6.750

in a table and I'm told to "find the formula for the exponential function in the form y=Pe^kx or y=Pa^x."

I'm not sure how to begin solving this problem. Any help, please?

 

[mmm4444bot]

Are you asked to find a model of best fit?

Are you in a class where they are using regression algorithms on calculators to find the best fit?

 

[Rumor]

No, no model of best fit was mentioned.

I was just given the values above and told to find the exponential function that fit the values.

 

[mmm4444bot]

The first time I tried to fit this data to an exponential model, it didn't fit exactly, so I thought maybe you were looking for a curve of best fit.

I must have made a mistake because it worked for me on my second attempt, just now.

I'll choose the given model that uses the natural base e.

y = P * e^(k*x)

It's easy to find the value of P because we know that e^0 = 1.

In other words, substitute the xy-pair (0, 2) into the given model, and solve for P.

Once you know P, substitute it, along with a different xy-pair, into the same model, and then solve for k.

Let me know if you need additional explanation of this process.

Cheers ~ Mark