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 $69,682.50 $72,429.27
2000 $78,943.50 $79,967.77
2005 $88,204.50 $88,290.88
2006 $90,056.70 $90,056.70
2007 $91,908.90 $91,857.83
2010 $97,465.50 $97,480.27

f(x) is exponential; an exponential function increases more slowly than a linear function.

f(x) is exponential; f(x) increased more overall than g(x).

g(x) is exponential; g(x) has a higher starting value and higher ending value.

g(x) is exponential; an exponential function increases faster than a linear function.

Answer 1

exponential functions get grow faster than any polynomial.

Over equal intervals, exponentials grow faster and faster. Unfortunately, your table does not have equal spacing, so you need to check your slopes to be sure.

Answer 2

Is this right