Question

Which equation of an exponential function has a graph that passes through the points
(1,5) and (2,15)?

Answer 1

Answer:

$y = \frac{5}{3} (3^{x} )$

Step-by-step explanation:

In general, $y = k(b^{x})$

Substitute x = 2, y = 15

(1)      $15 = kb^{2}$

Substitute x = 1, y = 5

(2)      $5 = kb^{1} = kb$

Divide equation (1) by equation (2)

$\frac{15 = kb^{2} }{5= kb }$

3 = b

Now substitute b = 3 in equation (2) to find k

5 = k(3)

$k = \frac{5}{3}$

Since we know the values for k and b, we now have the exponential function that passes thru (1, 5) and (2, 15)

$y = \frac{5}{3} (3^{x} )$