The tutor points out how to convert an exponential function m^x to e^kx.

Often, when thinking of an exponential function, one might imagine the form

y=e^(kx)

However,

y=m^x

is also exponential, since the independent variable is the exponent.

How do we convert from y=m^x to y=e^(kx)?

First, we realize that e^(lnm)=m, since ln and e are inverses. Next, we recall that (a^b)^c=a^(bc).

Therefore,

m^x=(e^(lnm))^x=e^(xlnm)

So y=m^x can be written as y=e^(xlnm).

HTH:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.