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.