Question

Find a formula for the exponential function passing through the points

Answer 1

Answer:

$y = 4*5^x$

Step-by-step explanation:

Given

$(x_1,y_1) = (-3,\frac{4}{125})$

$(x_2,y_2) = (1,20)$

Required

Determine the exponential equation

An exponential equation is of the form: $y = ab^x$

In: $(x_2,y_2) = (1,20)$

$20 = ab^1$

$20 = ab$ ---- (1)

In: $(x_1,y_1) = (-3,\frac{4}{125})$

$\frac{4}{125} = ab^{-3}$ --- (2)

Divide (1) by (2)

$20/\frac{4}{125} = \frac{ab}{ab^{-3}}$

$20/\frac{4}{125} = b^4$

$20*\frac{125}{4} = b^4$

$5*125 = b^4$

$625 = b^4$

Take 4th roots of both sides

$\sqrt[4]{625} = b$

$5 = b$

$b = 5$

Substitute $b = 5$ in $20 = ab$

$20 = a * 5$

Solve for a

$a = 20/5$

$a = 4$

Hence, the equation is:

$y = 4*5^x$