The table shows some values of an exponential function f and

The table shows some values of an exponential function, f, and a linear function, g. Find the equation for: f(x) and g(x) and use the functions to complete the table.

f(x) =_________

g(x) = ________

x f(x) g(x)

0 ___ 3

1 0.64 ____

2 0.512 5.4

3 _____ _____

4 0.32768 ______

5 ______ 9

Solution

f(x)

standard exponential function is given by

y = ab^x

where, a is the initial value and b is the rate of growth

b = next term / previous term

b = .512 / .64 = .8

a = .64/.8 = .8

hence, function f(x) = y = .8 (.8)^x

completing the table

x f(x)

0 .8

1 .64

2 .512

3 .41

4 .32768

5 .262

lets now find the linear function

in linear function rate of change is always constant

rate of change = y2-y1 / x2 - x1 = a - 3 / 1-0 ---- 1st equation

5.4 - a / 1 ------------2nd equation

setting both equations equal to each other

a-3 = 5.4 - a

2a = 8.4

a = 4.2

therefore , equation of g(x) is

g(x) = 1.2x + 3

completing the table

x g(x)

0 3

1 4.2

2 5.4

3 6.6

4 7.8

5 9