Question 399595
{{{y = ab^x}}}
If the graph passes through the two given points then the coordinates of those points should fit the equation. So
{{{(7) = ab^((1)) = ab}}}
and
{{{(49) = ab^((2)) = ab^2}}}
We now have two equations with two unknowns, a and b. We should be able to solve this system and find out what a and b are.<br>
We can use the Substitution method. Solving the first equation for a we get:
{{{7/b = a}}}
Substituting this into the second equation we get:
{{{49 = (7/b)b^2}}}
which simplifies as follows:
{{{49 = (7/b)(b^2/1)}}}
{{{49 = 7b^2/b}}}
49 = 7b
Dividing by 7 we get:
7 = b
Using {{{7/b = a}}} and the value we just found for b, we can find a:
{{{7/(7) = a}}}
1 = a
So a = 1 and b = 7. This makes the desired equation:
{{{y = (1)*(7)^x}}}
or
{{{y = 7^x}}}