<PRE><B>Question 1127693</B>
&lt;br&gt;(NOTE: You can ignore the solution by tutor MathLover1; the question asks for exponential functions -- not linear functions.)&lt;br&gt;
The general form of an exponential function is&lt;br&gt;
{{{y = ab^x}}}&lt;br&gt;
Given two points on the graph of an exponential function, the general process for finding the function is&lt;br&gt;
(1) use the coordinates of the two given points in the general form to get two equations in x and y;
(2) divide one equation by the other; that will eliminate a and give you an equation you can solve for b; and
(3) use the value of b in either equation to find the value of a&lt;br&gt;
Your example (a) turns out to have &quot;nice&quot; numbers; so I will demonstrate the process with the second example.&lt;br&gt;
(1)
{{{ab^(-1) = 7}}}
{{{ab^3 = 4}}}&lt;br&gt;
(2)
{{{b^4 = 4/7}}}
{{{b = (4/7)^(1/4) = .86944}}} to 5 decimal places&lt;br&gt;
(3)
{{{a(.86944)^(-1) = 7}}}
{{{a = 7(.86944) = 6.08608}}}&lt;br&gt;
The exponential function is&lt;br&gt;
{{{y = 6.08608(0.86944)^x}}}</PRE>