Find the equation of the exponential function represented by the table below:

Question

x. y

0. 4

1. 16

2. 64

3. 256

Answer 1

y = ab^x

Use coordinates to determine values of a and b as I have demonstrated in your previous post.

Answer 2

Notice that in the Y column, each new value is found by multiplying the previous value by 4. This tells us that the base of the exponential equation will be 4. Remember that the form you must end up with is a(b)^x. What we know so far is that b=4. To calculate a, just plug in an x value of 1 and 2, and see what adjustment must be made to get a true statement. For example a(4)¹=16 To make this true, a must be 4 because 4(4)¹=16.

Now let's confirm by plugging in 2. 4(4)²=64 is also true, so we have our answer. Our equation is 4(4)^x.

You can further confirm by plugging in 0 and 3: 4(4)⁰=4 So that one works.

Also 4(4)³= 256, so that one also works.

Best wishes!