Question 213273
Given:
{{{f(x) = Ca^x}}}
(2,45)
(5,1215)
I'll make 2 equations by substituting these values
(1) {{{45 = Ca^2}}}
(2) {{{1215 = Ca^5}}}
Multiply both sides of (1) by {{{a^3}}}
(1) {{{45a^3 = Ca^5}}}
And substituting again,
(2) {{{1215 = 45a^3}}}
{{{a^3 = 1215/45}}}
{{{a^3 = 27}}}
{{{a = 3}}}
(1) {{{45 = Ca^2}}}
{{{45 = C*9}}}
{{{C = 5}}}
The equation is
{{{f(x) = 5*3^x}}} answer
check:
{{{1215 = 5*3^5}}}
{{{1215 = 5*243}}}
{{{1215 = 1215}}}
OK
{{{45 = 5*3^2}}}
{{{45 = 5*9}}}
{{{45 = 45}}}
OK