exponential equation

Question

Write an exponential equation that goes through the given points and has the given asymptote.

6) (0, 7) and (3, 28) and has an asymptote at y = 4

Answer 1

The basic equation is y=a(b)^x

The information given about the asymptote of y=4 changes the equation to y=a(b)^x + 4

Plug in the first point

7=a(b)⁰ + 4 Subtract 4 from both sides

3=a(b)⁰ Simplify b⁰=1

3=a

Use the second point to find b

28=3(b)³ + 4 Subtract 4 from both sides

28=3(b)³ Divide both sides by 3

8=(b)³ Take the cube root of both sides

2=b

The equation is

y=3(2)^x + 4