How do you determine the formula for the graph of an exponential function given (0,3) and (2,6)?

1 Answer
Apr 5, 2018

y = 3e^(ln(sqrt2)x)

Explanation:

One form of an exponential function is:

y = y_0e^(kx)" [1]"

Substitute the point (0,3) into equation [1]:

3 = y_0e^(k0)

3 = y_0(1)

y_0 = 3 " [2]"

Substitute equation [2] into equation [1]:

y = 3e^(kx)" [1.1]"

Substitute the point (2,6) into equation [1.1]:

6 = 3e^(k(2))

2 = e^(2k)

ln(2) = 2k

k = 1/2ln(2)

k = ln(sqrt2)" [3]"

Substitute equation [3] into equation [1.1]:

y = 3e^(ln(sqrt2)x)