Write a linear function and an exponential function whose graphs pass through the points (0, 2) and (1,6).

Linear function:  Find the slope of the line segment that connects points (0,2) and (1,6).  Use the "slope-intercept form of the equation of a straight line:"

y=mx + b.  substitute your value for the slope, m.  It just so happens that (0,2) is the y-intercept, so substitute 2 for b.   Then write out y=mx+b.

Exponential function:  Use the exponential function model y=y0e^(kx).  You will need to determine the values of the initial value (y0) and the rate k.

first, look at the given point (0,2).  Substitute 0 for x and 2 for y.  This produces      2=y0e^0, so now you know that y0=the initial value=2.

Now write out y=y0e^(kt) again.  Subst. 2 for y0, 6 for y and 1 for x.
This is enough info to enable you to find the value of k.

Then write out the general equation in the form y=y0e^(kt).