Question 258412
Exponential functions have equations in the following form:
{{{y = k*a^x}}}
(Your book/teacher may use letters other than k and a but the basic form should be the same.)
With the two ordered pairs we have two sets of x and y values that should fit the equation:
{{{0.5 = k*a^0}}} and {{{3 = k*a^1}}}
We can use this system to solve for k and a. The first equation, since anything but zero to the zero power is a 1, simplifies to:
{{{0.5 = k*1}}}
or
{{{0.5 = k}}}
Already we have the k for our function. Now we can use this value for k and the second equation to find a:
{{{3 = (0.5)a^1}}}
Since {{{a^1 = a}}}:
{{{3 = (0.5)a}}}
Multiplying both sides by 2 we get:
{{{6 = a}}}
With k = 0.5 and a = 6 our exponential function is:
{{{y = (0.5)6^x}}}