Question

The exponential function f, whose graph is given below, can be written as​

Answer 1

f(x) = 2·3^x

Explanation:

We have the general equation of exponential functions as

y= a*b^x

We are given that the point (0,2) is on the graph so

when x= 0, y= 2

If we substitute in the general equation we see that

2 = a*b^0, any number to the power 0 is 1

2 = a

We were also given that point (1, 6 ) is on the graph;

If we substitute in our new found equation we see that

y=2·b^x

6 = 2·b^1 , any number to the power 1 is itself and

divide both sides by 2

3 = b

f(x) = 2·3^x