Question 1148671
Find a formula for the exponential function passing through the points (-1,3/5) and (3,375).
<pre>The other person's answer is WRONG!
{{{matrix(1,3, y, "=", ab^x)}}}
{{{matrix(1,3, 3/5, "=", ab^(- 1))}}} ------ Substituting (- 1, {{{3/5}}}) for (x, y)
{{{matrix(1,7, a, "=", (3/5)/(1/b), "=", (3/5) * b, "=", 3b/5)}}} ------- eq (i)


{{{matrix(1,3, y, "=", ab^x)}}}
{{{matrix(1,3, 375, "=", ab^3)}}} ----- Substituting (3, 375) for (x, y)
{{{matrix(1,3, a, "=", 375/b^3)}}} ------- eq (ii)


This then results in: {{{matrix(1,3, 3b/5, "=", 375/b^3)}}}
{{{matrix(1,3, 3b^4, "=", 5(375))}}}------- Cross-multiplying
{{{matrix(1,5, b^4, "=", 5(375)/3, "=", 625)}}}
{{{matrix(1,5, b, "=", root (4, 625), "=", 5)}}}
{{{matrix(1,5, a, "=", 3(5)/5, "=", 3)}}} ------- Substituting 5 for b in eq (i)
Exponential function: {{{highlight_green(matrix(1,3, f(x), "=", 3(5)^x))}}}</pre>