Question

Write an exponential function in the form y = ab that goes through points (0,4) and (2, 196).

Answer 1

Answer:

y = 4$(7)^{x}$

Step-by-step explanation:

The form of the exponential function is y = a $b^{x}$

Use the given points to solve for a and b

Using (0, 4 ), then

4 = a$b^{0}$ ( $b^{0}$ = 1 ), thus a = 4

y = 4 $b^{x}$

Using (2, 196 ), then

196 = 4b² ( divide both sides by 4 )

49 = b² ( take the square root of both sides )

b = $\sqrt{49}$ = 7

y = 4$(7)^{x}$ ← exponential function