To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function:
f
(
x
)
=
x
2
f
(
x
)
=
x
2
Horizontal Shift: Right
5
5
Units
Vertical Shift: Up
2
2
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
Answer:
see below
Step-by-step explanation:
4 ^(3x-1)=3
Take the natural log of each side
ln(4 ^(3x-1))= ln (3)
We know that ln ( a^b) = b ln a
(3x-1) ln 4 = ln 3
Divide each side by ln 4
3x-1 = ln(3)/ (ln4)
Add 1 to each side
3x = ln(3)/ ln (4) +1
Divide by 3
x =1/3 [( ln 3)/ ln (4)] + 1/3
x = .792461
Answer:
P(t) = 3000 * 4^(t/10)
Step-by-step explanation:
There is more than one way to get an exponential function out of the information given. The way the question is worded, however, seems to suggest the following type of answer:
One general form of the exponential function is y = a·bx, where a is the initial value, and b is the growth or decay factor. So right away we can say that a = 2300.
Now for the growth factor. When something is increasing or decreasing by a certain percentage, we are adding or subtracting that percentage to the 100% (which is equal to 1) that exists currently. So here we're increasing by 11%, or 0.11. Then the growth factor b is (1 + 0.11), or 1.11.
Answer:200
Step-by-step explanation:
