Question

Show that an exponential model fits the data. Then write a recrusive rule that models the data.

n = 0, 1, 2, 3, 4, 5,
f(n) = 0.75, 1.5, 3, 6, 12, 24.

(this is a rectangular graph ^)​

Answer 1

Exponential function:

• f(x) = abˣ

Use the given data to determine the function.

• f(0) = ab⁰ = a*1 = a ⇒ a = 0.75

• b = 2 as each of the f(n) is twice the previous one in series.

The model is:

• f(n) = 0.75*2ⁿ

Recursive rule to reflect this is:

• f(0) = 0.75
• f(n) = 2*f(n-1)