Answer:
- x = log(y/4)/log(1.0256)
- your answer for y=12 is correct
Step-by-step explanation:
The question is asking you to solve ...
y = f(x)
for x. (In other words, find the inverse function.)
You already did this using a constant for y. Do the same thing with y instead of the constant.
y = 4(1.0256^x)
y/4 = 1.0256^x . . . . . . . divide by 4
log(y/4) = x·log(1.0256) . . . . . take logs
log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x
Now, you have a model for x in terms of y, which is what the question is asking for.
x = log(y/4)/log(1.0256) . . . . . . . exact expression
When y=12, this is ...
x = log(12/4)/log(1.0256) ≈ 43.46 . . . . weeks
_____
This is a linear equation in log(y), so can be written as such:
x = 91.0912·log(y) -54.8424 . . . . . approximate expression
Answer:
See Explanation
Step-by-step explanation:
Given
New function: 
We can assume the parent function to be:
The new function can be represented as:
Where
A = Vertical stretch factor
B = Period
C = Right shift
By comparison:
to
Solve for B
Using the calculated values of 
This implies that, the following transformations occur on the parent function:
- <em>Vertically stretched by </em>
<em /> - <em>Horizontally compressed by </em>
<em /> - <em>Right shifted by </em>
<em />
1024 , multiply the last number by 4
To get from 8.4 to 10 in multiplication, we need to multiply 8.4 by 10/8.4
That means that if we multiply 30 by 10/8.4 we get the answer
which is 35,714
The same with the other
8.4 times 100/30 = 28
