Question

(1) The geometric model g of n for f of n can be written as g of n= ab^n where a and b are constants. Use the given data to write two equations that can be used to find the values for constants a and b in the expression for g of n

n- 2 4 5
F of n- 3 17 24

Answer 1

Using two data points from a geometric model, two equations can be set up: 3 = ab^2 and 17 = ab^4. These allow for solving the constants a and b by creating a ratio to eliminate a and then solving for a with one of the equations.

Step-by-step explanation:

To find the constants a and b for the geometric model g of n, given by the equation g(n) = ab^n, we can use the given data points: when n = 2, f(n) = 3; and when n = 4, f(n) = 17.

We can set up two equations based on these points:

• For n = 2: 3 = ab^2
• For n = 4: 17 = ab^4

With these equations, you can solve for a and b by first finding a ratio of the second equation to the first in order to cancel out a and solve for b, and subsequently finding a using either of the original equations.