A(x) = P(1.02)^x
A(x) = P(1 + 0.02)^x
A(x) = P(1 + r)^x
Therefore rate of change = 0.02 = 2%.
Answer:
The largest number of elephants which Daniel could have is 2007
Step-by-step explanation:
The theorem behind it is if u and v are coprime positive interger then
N= 2UV -u-v
Where u = 28 v=37
N= 2×28×37- 28-37
N= 2007
I know you got this from Khan Academy, and so the answer is $9.81. You probably don't care about how it is done, and you probably just want to put the answer and be done, but I will show you. You have to take the original price of $9 and multiply it with 9%, or 0.09, to get the amount of your tip. add the 9%, or $81. You can also just do 9*109%, or 9*1.09, to put these two steps together and add the original price and the tip.
Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
