Question

Write an exponential function in the form y = ab that goes through points (0,18)

Answer 1

Answer:

$18 = ab^0 =a$

And using the second point we have this:

$288= 18 b^2$

If we divide both sides by 18 we got:

$16 = b^2$

And taking the square roof of 16 we got:

$b =\pm \sqrt{16} =\pm 4$

But on this case the negative solution not makes sense since the function is increasing so then the correct exponential function that pass through the points (0,18) and (2,288) is:

$y = 18 (4)^x$

Step-by-step explanation:

We want to construct an exponential function given by this general form:

$y = ab^x$

And we know that the function needs to pass for two points (0,18) and (2,288). Using the first point we have this:

$18 = ab^0 =a$

And using the second point we have this:

$288= 18 b^2$

If we divide both sides by 18 we got:

$16 = b^2$

And taking the square roof of 16 we got:

$b =\pm \sqrt{16} =\pm 4$

But on this case the negative solution not makes sense since the function is increasing so then the correct exponential function that pass through the points (0,18) and (2,288) is:

$y = 18 (4)^x$