Question

Two different businesses model their profits over 15 years, where x is the year, f(x) is the profits of a garden shop, and g(x) is the profits of a construction materials business. Use the data to determine which function is exponential, and use the table to justify your answer.


x f(x) g(x)
1995 $14,170.20 $11,008.31
2000 $19,396.20 $16,174.82
2005 $24,622.20 $23,766.11
2006 $25,667.40 $25,667.40
2007 $26,712.60 $27,720.79
2010 $31,938.60 $34,920.21

Answer 1

The function g(x) is exponential.

What is a Function ?

A function is a mathematical Statement used to find relation between independent and dependent variable.

The data is given for the two functions

From observing the data it can be understood that

g(x) is represented as an exponential function

g(x) = abˣ

The data given is

At year = 1995, x =0 and y = 11008.31

At year = 2000, x =5 and y = 16,174

11008.31 = a b⁰

a = 11008.31

g(x) = 11008.31 bˣ

16174 = 11008.31 bˣ

b = 1.08

g(x) = 11008.31 (1.08)ˣ

At 2005 , x = 10

g(x) = 11008.31 (1.08)¹⁰

g(x) = 23766.11

Therefore the table justifies our answer.

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