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

$7000 \: = a \times 1 = a$

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

$\frac{1120}{7000} = {b}^{2} \\ \sqrt{ \frac{1120}{7000} } = b \\ b = 0.4$