1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mylen [45]
3 years ago
13

The function f(x)=21,500(0.86)^x models the value of a car after x years. What is the yearly depreciation rate of the value of t

he car?
Mathematics
1 answer:
Serjik [45]3 years ago
3 0

Answer:

The car loses 14 percent of its value each year.

Step-by-step explanation:

subtract .86 from 1 to get the value of depreciation

You might be interested in
How to differentiate ?
Bas_tet [7]

Use the power, product, and chain rules:

y = x^2 (3x-1)^3

• product rule

\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2)}{\mathrm dx}\times(3x-1)^3 + x^2\times\dfrac{\mathrm d(3x-1)^3}{\mathrm dx}

• power rule for the first term, and power/chain rules for the second term:

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(x-1)^2\times\dfrac{\mathrm d(3x-1)}{\mathrm dx}

• power rule

\dfrac{\mathrm dy}{\mathrm dx} = 2x\times(3x-1)^3 + x^2\times3(3x-1)^2\times3

Now simplify.

\dfrac{\mathrm dy}{\mathrm dx} = 2x(3x-1)^3 + 9x^2(3x-1)^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2 \times (2(3x-1) + 9x) \\\\ \boxed{\dfrac{\mathrm dy}{\mathrm dx} = x(3x-1)^2(15x-2)}

You could also use logarithmic differentiation, which involves taking logarithms of both sides and differentiating with the chain rule.

On the right side, the logarithm of a product can be expanded as a sum of logarithms. Then use other properties of logarithms to simplify

\ln(y) = \ln\left(x^2(3x-1)^3\right) \\\\ \ln(y) =  \ln\left(x^2\right) + \ln\left((3x-1)^3\right) \\\\ \ln(y) = 2\ln(x) + 3\ln(3x-1)

Differentiate both sides and you end up with the same derivative:

\dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac2x + \dfrac9{3x-1} \\\\ \dfrac1y\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{15x-2}{x(3x-1)} \times x^2(3x-1)^3 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = x(15x-2)(3x-1)^2

7 0
2 years ago
Simplify: 3(4x+1)<br><br> Thank you so much
Anvisha [2.4K]

Answer:

the answer is 12x +3

Step-by-step explanation:

6 0
3 years ago
What are the rate of change and the initial value of the function represented by the graph?
Norma-Jean [14]

Answer:D

Step-by-step explanation:

7 0
2 years ago
Is 0.333 a natural number?
NeX [460]

Answer:

No, 0.333 is a rational number, not a natural number

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
If i have 2 apples and eat one and give the other away how many are their.
Sphinxa [80]
There will be 0 apples left since you have one away and ate the other
5 0
3 years ago
Other questions:
  • Jim bought a fishing rod for $42. The price was 70% of the original price. What was the original price?
    14·2 answers
  • I need help simplify 2a^0
    6·2 answers
  • Which set of ordered pairs demonstrates a function? A (-2, -4), (-1, -2), (1, 2), (2, 4) B (-2, 4), (1, 2), (1, -2), (2, -4) C (
    13·2 answers
  • (Day 8) Find the value of each variable. The dot represents
    7·1 answer
  • (08.01)Jenni is surveying shoppers about their use of the new customer service center in a store. Which question in her survey i
    10·1 answer
  • Need help figuring out the answer got any tips??
    6·2 answers
  • Which is equivalent to 80^1/4x
    15·1 answer
  • At a marlin fishing tournament, the winning fish was 342 5/16 pounds. The average fish caught weighed 167 3/8 pounds. What is th
    9·2 answers
  • DIRECTION: Create your own mathematical world problem that involves division of fraction. you base your problem from the given d
    15·1 answer
  • The graph of a polynomial function has zeroes 0 (multiplicity 2) , 1 (multiplicity 2), and 5/2 (multiplicity 2). Write a functio
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!