Question

Finding the equation

Answer 1

Answer:

p(x): y-intercept is 4; the base is 3; the equation is p(x) = 4(3^x)

q(x):  y-intercept is 4; the base is 2; the equation is p(x) = 4(2^x)

Step-by-step explanation:

The y-intercept of both graphs is 4

The standard exponential function equation is

y = ab^x

We need to find a and b for each function.

For each graph, we use two points to find a and b in the standard exponential function equation.

p(x)

y = ab^x

Use point (0, 4)

4 = ab^0

4 = a * 1

a = 4

y = 4(b^x)

Use point (1, 12)

12 = 4(b^1)

b = 12/4

b = 3

The base is 3.

p(x) = 4(3^x)

q(x)

y = ab^x

Use point (0, 4)

4 = ab^0

4 = a * 1

a = 4

y = 4(b^x)

Use point (1, 8)

8 = 4(b^1)

b = 8/4

b = 2

The base is 2.

q(x) = 4(2^x)