We'll need to know what help you need. If you need a place to start, that would be to find the definitions you have been given for each type of function, which may or may not be what I would guess.Learning online on my own is proofing difficult... appreciate any help... cheers...
If a function f has values f(5)=12 and f(10)=18 , find f(20)=(?) if,
a) Exponential Function;
b) Linear Function;
c) Power Function.
We'll need to know what help you need. If you need a place to start, that would be to find the definitions you have been given for each type of function, which may or may not be what I would guess.
Once you've told us the three forms (for instance, the linear function is probably something like y = ax + b), then in each case you will be replacing x and y with the two given pairs, resulting in a pair of equations you can solve for the parameters (e.g. a and b).
Please show whatever you can do and what you have been taught, and we can discuss the details.
The work looks good without checking every detail; let's check it out:I have solved the Exponential and the linear, now trying the power function, applying the formula f(x)=axk, but I am having some trouble in solving it... thank you Dr. Peterson
That is what I have for the power function so far... but it's wrong somewhere... tks...
Power Function: y = Ax^k
f(5) = 12
12 = A(5)^k
f(10) = 18
18 = A(10)^k
Solve 2 equations, 2 unknowns:
12 / 5^k = 18 / 10^k
12 / 18 = 10^k / 5^k
2/3 = 2^k•5^k / 5^k
2/3 = 2^k
k = log(base 2) (2/3)
k = ln(2/3) / ln(2)
k = (ln2 - ln3) / ln2
k = 1 - ln3/ln2
k = -0.585
A = 12 / 5^(-0.585)
A = 30.8
y = 30.8x^(-0.585)
y(20) = 30.8(20)^(-0.585)
y(20) = 5.34