Answer:
[tex]y = \frac{5}{3} (3^{x} )[/tex]
Step-by-step explanation:
In general, [tex]y = k(b^{x})[/tex]
Substitute x = 2, y = 15
(1) [tex]15 = kb^{2}[/tex]
Substitute x = 1, y = 5
(2) [tex]5 = kb^{1} = kb[/tex]
Divide equation (1) by equation (2)
[tex]\frac{15 = kb^{2} }{5= kb }[/tex]
3 = b
Now substitute b = 3 in equation (2) to find k
5 = k(3)
[tex]k = \frac{5}{3}[/tex]
Since we know the values for k and b, we now have the exponential function that passes thru (1, 5) and (2, 15)
[tex]y = \frac{5}{3} (3^{x} )[/tex]
