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(B) (i) 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 gn

(B) (i) The geometric model g of n for f of n can be written as g of n= ab^n, where-example-1
User GrGr
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i) Two models for f_n: arithmetic and geometric (g_n = ab^n).

ii) Values for a and b found using given data (a=1, b=3).

iii) Constant k calculated from the g_n model (k=243).

i) The table in the image shows values for a sequence f at selected values of n, where k is a constant. The data in the table can be used to find two models for f_n: an arithmetic model (a_n) and a geometric model (g_n).

ii) The geometric model g_n for f_n can be written as g_n = ab^n where a and b are constants. To find the values for constants a and b, we can use the given data to write two equations.

The first equation is:

3 = ab^2

The second equation is:

24 = ab^5

We can solve these equations to find that a = 1 and b = 3.

iii) Using the geometric model g_n, we can find the value of the constant k in the table above. The equation for k is:

k = g_5 = ab^5 = (1)(3)^5 = 243

Therefore, the value of k is 243.

User Webby Vanderhack
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