1 point Find a possible formula for f x in 18 and f 2 88 an

(1 point) Find a possible formula for f (x) in 1-8 and f (2) = 88 and: (a) f(x) is a linear function. f(x) (b) f(x) is a power function. f(x) c) f(x) is an exponential function, f(x) = *j

Solution

points on curve are (1,8),(2,88)

(a)

linear function:

f(x) -8 =[(88-8)_/(2-1)](x-1)

=>f(x) -8 =80(x-1)

=>f(x) -8 =80x-80

=>f(x) =80x -72

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(b)

general power function is f(x) =ax^b

f(1) =a*1^b =8

=>a=8

f(x) =8x^b

=>f(2) =8*2^b=88

=>2^b=88_/8

=>2^b=11

=>b =(ln₂11)

power function:f(x) =8x^(ln₂11)or f(x) =8x^3.45943

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(c)

general exponential equation is f(x)=ab^x

f(1) =ab¹ =8

=>ab=8

f(2) =a*b² =88

=>ab²=88

ab²_/ab=88_/8

=>b=11

ab=8, b=11

=>a*11=8

=>a=8_/11

exponential equation is f(x)=(8_/11)11^x or   f(x)=8*11^x-1