Find a possible formula for f if f2 40 and f4 160 if f is

Find a possible formula for f if f(2) = 40 and f(4) = 160 if f is (a) linear (b) exponential (c) a power function

Solution

f(2)=40   and f(4)=160

a. linear

Here we have two points (2,40) and (4,160)

y=mx+b

40=2m+b

160=4m+b

Solving these equations we get

m=60, b=-80

Therefore the required equation is y=60x -80

b. exponential

y=a b^x

40= a b²

160= a b⁴

Dividing these equations we get

b=2,a=10

Required equation is y= 10*2^x

c. a power function

y= k *xⁿ

40= k*2ⁿ

160= k* 4ⁿ

dividing these equations,we get

4= 2ⁿ

n=2

40= k * 2²

k=10

y= 10* x²