ANSWER
$16,384
EXPLANATION
From the question we have that,
Nadir saves $1 the first day of a month, $2 the second day, $4 the third day, and so on.
This forms a geometric sequence,
The first term of this sequence is
The common ratio is
The general term of a geometric sequence is given by the formula:
To find the 15th term, we plug in a=1, r=2 and n=15.
The amount he will save on the 15th day is $16,384
Answer:
C. 2
Step-by-step explanation:
Gradient =
Gradient =
Gradient = 2
Answer:
Step-by-step explanation:
So, there are two logarithmic identities you're going to need to know.
<em>Logarithm of a power</em>:
So to provide a quick proof and intuition as to why this works, let's consider the following logarithm:
Now if we raise both sides to the power of c, we get the following equation:
Using the exponential identity:
We get the equation:
If we convert this back into logarithmic form we get:
Since x was the basic logarithm we started with, we substitute it back in, to get the equation:
Now the second logarithmic property you need to know is
<em>The Logarithm of a Product</em>:
Now for a quick proof, let's just say:
Now rewriting them both in exponential form, we get the equations:
We can multiply a * c, and since b^x = a, and b^y = c, we can substitute that in for a * c, to get the following equation:
Using the exponential identity: , we can rewrite the equation as:
taking the logarithm of both sides, we get:
Since x and y are just the logarithms we started with, we can substitute them back in to get:
Now let's use these identities to rewrite the equation you gave
As you can see, this is a log of products, so we can separate it into two logarithms (with the same base)
Now using the logarithm of a power to rewrite the log(x^2) we get: