Question

Write an exponential function for a graph that passes through the points (2,16) and (3,32).

Answer 1

Answer:

$y = 4(2^{x} )$

Step-by-step explanation:

The general form for an exponential function is $y = kb^{x}$

When x = 2,  y = 16    So, $16 = kb^{2}$    

and when x = 3,  y = 32    So, $32 = kb^{3}$

Divide  $\frac{32}{16} = \frac{kb^{3} }{kb^{2} }$

2 = b

Now, $16 = k2^{2}$

16 = 4k

k = 4

Therefore, the exponential function is $y = 4(2^{x} )$