Question

An exponential function f(x) = ab^x f (x) = passes through the points (0, 7000) and (2, 1120). What are the values of A and B

Answer 1

`a =7000`

`b = 0.4`

Step by step:

Firstly, we should substitute the points where x is equal to 0 so that we can obtain the a value

`7000 = a {b}^(0)`

And because anything to the power of 0 is 1

`7000 \: = a * 1 = a`

Now that we have the value for a, we can substitute it into the 2nd equation to find b

`1120 = 7000 {b}^(2)`

Finally, we rearrange to make b the subject

`(1120)/(7000) = {b}^(2) \\ \sqrt{ (1120)/(7000) } = b \\ b = 0.4`