Getting Equation For Exponential Function From A Table Of Values

[AlphaCloud]

This is an intro into logarithms which I do understand it's just this one example from our class notes that's confusing me.

The question/example set is this:


I've tried using Youtube and looking over class notes of how to get an equation for an exponential function but can't seem to find the right solution as these appear to use translations which I can't find out how it was done.

The work I was able to get done so far is here:


What would I be missing here or is there any good resource I can refer to to figure out how to get the different transformations?

Thank you in advance

 

[AlphaCloud]

Ok so I think I solved this but just want to make sure I got it right.

The first function would be y=2^(x+1). My theory behind it is since 2^0 is 1 but in the table it's 2 and all the values are shifted 1 up so it means that I'd have to add 1 to the x in the exponent position. 2^x + 1 wouldn't work as x = 1 would not yield 8.

For the second one I checked to see if it's a parabola thing(idk the name) and the pattern of incrementing shows it goes up by 2 so it has to be x^2 and then a matter of checking x^2 + what gives me the y value which in this case was 5.

I'm hoping I got on the right track here

 

[Cubist]

Table a) seems incorrect to me. I think that when x=4 then y should equal 512 (and not 256 as stated).

I suggest that you consider looking at an equation of the form y=a*b^x where "a" and "b" are constants that you need to find.

 

[AlphaCloud]

Table a) seems incorrect to me. I think that when x=4 then y should equal 512 (and not 256 as stated).

I think this could be the problem

I suggest that you consider looking at an equation of the form y=a*b^x where "a" and "b" are constants that you need to find.

that's what I tried for the first question, I assume that the answer given was simplified as when I solve it I get 2*4^x and 4 can be broken down so
2*2^2x and then the 2*2 exponents can be added so I get 2^1 * 2^2x so it turns into 2^(2x+1) which appears to match up with the solution.

That would make sense right?

 

[Dr.Peterson]

This is an intro into logarithms which I do understand it's just this one example from our class notes that's confusing me.

The question/example set is this:
View attachment 30753

I've tried using Youtube and looking over class notes of how to get an equation for an exponential function but can't seem to find the right solution as these appear to use translations which I can't find out how it was done.

The work I was able to get done so far is here:
View attachment 30754

What would I be missing here or is there any good resource I can refer to to figure out how to get the different transformations?

Thank you in advance

For (c), you might swap the columns temporarily and try to find x as a function of y. Then solve for y.

That is very appropriate for an intro to logarithms ...

 

[Steven G]

b) is not an exponential function! Why not? Because as x increases by 1, to go from one y value to the next you do not multiply the previous y by some constant.

For example, if the y values went from 3 to 15 to 75 to 375, then this would be exponential.