Question

Given the two points (3,1) and (5,4), find the equation of the exponential function that passes through these two points.

Answer 1

Answer:

y = $\frac{1}{8}$$(2)^{x}$

Step-by-step explanation:

For an exponential of the form y = a$(b)^{x}$

Use the given points to find a and b

Using (3, 1 ), then

1 = ab³ → (1)

Using (5, 4 ), then

4 = a$b^{5}$ → (2)

Divide (2) by (1)

$\frac{ab^5}{ab^3}$ = 4

b² = 4 ⇒ b = $\sqrt{4}$ = 2

Substitute b = 2 into (1)

a2³ = 1

8a = 1 ( divide both sides by 8 )

a = $\frac{1}{8}$

Thus exponential function is

y = $\frac{1}{8}$$(2)^{x}$