Question

Find a possible formula for the function represented by the data. The value for the base should be correct to one decimal place. X 0 1 2 3 f left-parenthesis x right-parenthesis 4.80 5.76 6.91 8.29

Answer 1

Since clearly we can see that is not linear relation( straight line), let us find ratios of consecutive terms.

`(f(1))/(f(0)) =  (5.76)/(4.8) = 1.2`

`(f(2))/(f(1))  = (6.91)/(5.76) =1.2`

`(f(3))/(f(2)) =(8.29)/(6.91)  = 1.2`

This follows f(1)= 1.2*f(0)

f(2) = 1.2*f(1) = 1.2*1.2*f(0) =
`1.2^(2) * f(0)`

f(3) = 1.2*f(2) =
`1.2*1.2^(2) *f(0) = 1.2^(3) * f(0)`

Hence formula is f(x) =
`1.2^(x) * f(0)`

f(x) =
`4.8*(1.2)^(x)`