Answer:
f(x) = 26500 * (0.925)^x
It will take 7 years
Step-by-step explanation:
A car with an initial cost of $26,500 depreciates at a rate of 7.5% per year. Write the function that models this situation. Then use your formula to determine when the value of the car will be $15,000 to the nearest year.
To find the formula we will use this formula: f(x) = a * b^x. A is our initial value which in this case is $26500. B is how much the value is increasing or decreasing. In this case it is decreasing by 7.5% per year. Since the car value is decreasing we will subtract 0.075 from 1. This will result in the formula being f(x) = 26500 * (0.925)^x. Now to find the value of the car to the nearest year of when the car will be 15000 we plug 15000 into f(x). 15000 = 26500 * (0.925)^x. First we divide both side by 26500 which will make the equation: 0.56603773584=(0.925)^x. Then we will root 0.56603773584 by 0.925. This will result in x being 7.29968 which is approximately 7 years.
Answer:
the geometric series is a(n) = -12(3)^(n-1)
Step-by-step explanation:
"Triple" denotes multiplication by 3. Thus, the common factor here is 3.
The general formula for a geometric series is a(n) = a(1)(r)^(n-1), where a(1) is the first term, r is the common ratio.
Here, we have a(n)= (-12)(3)^(n-1) = -972.
We need to solve this for n, which represents the last term.
The first step towards solving for n is to divide both sides by -12:
3^(n-1) = 81
To solve for n-1, rewrite 81 as 3^4. Then we have:
3^(n-1) = 3^4, implying that (n-1) = 4 and that n = 5.
Then we know that it is the 5th term that equals -972.
In summary, the geometric series is a(n) = -12(3)^(n-1).
First, multiply 4*2x-4*-5= 8x-20.
Second, add 15 to 8x-20
Third, that would equal 8x-20+15=11
Fourth, 15+-20= -5
Fifth, 8x-5=11
Sixth, add +5 to -5 and +5 to 11= 8x=16
Last, do 8x/8x and 16/8x
The answer is x=2
Answer:
(a) B. G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.
(b) Every function of the form 
is an antiderivative of 8x
Step-by-step explanation:
A function <em>F </em>is an antiderivative of the function <em>f</em> if
for all x in the domain of <em>f.</em>
(a) If 
, then 
is an antiderivative of <em>f </em>because
Therefore, G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.
Let F be an antiderivative of f. Then, for each constant C, the function F(x) + C is also an antiderivative of <em>f</em>.
(b) Because
then is an antiderivative of . Therefore, every antiderivative of 8x is of the form for some constant C, and every function of the form is an antiderivative of 8x.
Distribute
-2(x+6)+3
-2x-12+3
-2x-12+3=-11x+4(x+4)
Distribute
4(x+4)
4x+16
-2x-12+3=-11x+4x+16
Combine Numbers && Variables
-2x-9=-7x+16
Add The 7 Over To The -2x
5x-9=16
Add 9 Over To 16
5x=25
x=5
So 5 Is Your Answer
~Hope This Helps :)
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