1. Find the equation of the function f(x) passing through the points (3,8) and (10,22) if f(x) is?

Question

2. Find the equation of the function f(x) passing through the points (3,8) and (10,22) if f(x) is

a) linear function

b) exponential function

c) power function

Any help is greatly appreciated. Thank you.

Answer 1

Favorite Answer

Linear:

y=mx+q

8=3*m+q and

22=10*m+q

m=(8-q)/3)

22=10((8-q)/3)+q --> q=2

m=2

y=2x+2

__________________________

Exponential:

y=e^(x+a)+c --> y=(e^x)*(e^a)+c

8=(e^3)*(e^a)+c

22=(e^10)*(e^a)+c

c=8-(e^3)*(e^a)

22=(e^10)*(e^a)+8-(e^3)*(e^a)

c=8-(e^3)(e^a)

e^a=14/(e^10-e^3)=0.000636179

a=ln(^a)=-7.360030372

c=8-0.012777996=7.987222003

y=e^(x-736..)+7.98..

___________________________

Power:

y=x^(a)+b

8=3^a+b

22=10^a+b

y=x^1.254+4.034389522

Huh!!!! This last has been really hard for me! I resolved it by iteration...in limit of 0.001 is correct. If you want more precision, start to iterate from 1.2541 and 1.2549 as extremes.

I suggest you (it's not a judgement, just a suggestion, forgive me if i say wrong) to apply yourself: i would dislike to make someone else's work, leaving him not to apprend.

In the exponential i left ".." instead of complete result, but the numbers are written just before.

Nice question.

Source(s): wikipedia.it