Respuesta :
Answer:
[tex] 18 = ab^0 =a[/tex]
And using the second point we have this:
[tex] 288= 18 b^2[/tex]
If we divide both sides by 18 we got:
[tex] 16 = b^2[/tex]
And taking the square roof of 16 we got:
[tex] b =\pm \sqrt{16} =\pm 4[/tex]
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:
[tex] y = 18 (4)^x[/tex]
Step-by-step explanation:
We want to construct an exponential function given by this general form:
[tex] y = ab^x[/tex]
And we know that the function needs to pass for two points (0,18) and (2,288). Using the first point we have this:
[tex] 18 = ab^0 =a[/tex]
And using the second point we have this:
[tex] 288= 18 b^2[/tex]
If we divide both sides by 18 we got:
[tex] 16 = b^2[/tex]
And taking the square roof of 16 we got:
[tex] b =\pm \sqrt{16} =\pm 4[/tex]
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:
[tex] y = 18 (4)^x[/tex]
