Hello!
The parent function, y = ln(x), has a vertical and horizontal translation.
y = ln(x - h) + k | In this equation, h is the vertical shift, and k is the horizontal shift.
If ln(x - k), then the graph is translated right k units.
If ln(x + k), then the graph is translated left k units.
If ln(x) + h, then the graph is translated up h units.
If ln(x) - h, then the graph is translated down h units.
Therefore, the graph of y = ln(x - 7) + 3 is translated 3 units up and 7 units to the right, which is choice D.
Answer:
an = 115 + (n - 1) (-6)
a25 = - 29
Step-by-step explanation:
We use the definition for the nth term of an arithmetic sequence:
an = a1 + (n - 1) d
a5 = 91 = a1 + (5 - 1) d
91 = a1 + 4 d
a20 = 1 = a1 + (20 - 1) d = a1 + 19 d
1 = a1 + 19 d
now we subtract term by term one expression from the other
90 = 4 d - 19 d
90 = - 15 d
divide both sides by -15 to isolate d
d = 90 / (-15) = -6
Now we can calculate what a1 is using for example:
1 = a1 + 19 d
1 = a1 - 114
add 114 to both sides:
115 = a1
Then our general expression for the sequence is:
an = 115 + (n - 1) (-6)
We can now use it to calculate the value of a25:
a25 = 115 + (24) * (-6) = -29
C because both equations make -8
Answer:
Step-by-step explanation:
For each consecutive year after that, their profit increased by 12%. The growth is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the profit made after t years.
t represents the number of years.
P represents the initial profit made.
r represents rate of increase.
From the information given,
P = 2.4 × 10^6
r = 12% = 12/100 = 0.12
t = 4 years
Therefore,
A = 2.4 × 10^6(1 + 0.12)^4
A = 2.4 × 10^6(1.12)^4
A = 3776446.5
Answer:
Formal thinking
Step-by-step explanation:
