I just don't understand this question:

h(t)=A*b^x h(3)=4 h(5)=40
Solve for b
Would you plug 3 into the x and set it equal to 4? (4=A*b^3) How would you solve for that because in the next question they go on to ask you to solve for A using the b you found...

Almost looks like your textbook has made a typo.

Yes, if this is a typo, you should "plug 3 into x and set it equal to 4".

You have two constants,a and b, and two equations to solve them.

H(3)=4=Ab^3
H(5)=40=Ab^5

divide the first equation into the second.

40/4=Ab^5/Ab^3

10=b^2
solve for b, then go back and substitute and solve for A.

To solve for b, we can start by dividing the equation h(5) / h(3), which gives us:

h(5) / h(3) = 40 / 4

Simplifying this equation further, we get:

10 = b^2

To solve for b, we can take the square root of both sides:

√10 = b

Remember that there are two possible solutions for b, as both the positive and negative square root of 10 satisfy the equation. So the two possible values for b are √10 and -√10.

Now that we have the value of b, we can plug it back into one of the original equations, such as h(3) = A * b^3, to solve for A. Let's use the positive square root of 10, √10:

h(3) = 4 = A * (√10)^3

Simplifying further, we get:

4 = A * 10^(3/2)

To solve for A, we can divide both sides by 10^(3/2):

4 / 10^(3/2) = A

Using a calculator to evaluate 10^(3/2) ≈ 31.62, we can simplify the equation:

4 / 31.62 ≈ A

So, we find that A ≈ 0.1264.

Therefore, the solutions for the given equations are approximately A ≈ 0.1264 and b ≈ √10.