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
Naddik [55]
3 years ago
11

**50 POINTS!!! WILL GIVE BRAINLIEST!!!**

Mathematics
1 answer:
lorasvet [3.4K]3 years ago
5 0
<h3>Given</h3>

The values of two houses (in thousands of dollars)

\left[\begin{array}{c|cccc}\text{year}&0&1&2&3\\\text{value 1}&286&294.58&303.4174&312.51992\\\text{value 2}&286&295&304&313\end{array}\right]

<h3>Find</h3>

A) the nature of the function, linear or exponential, that can be used to model the value after x years

B) the actual function f(x) that can be used in each case

C) f(25) for each house. Is there a significant difference?

<h3>Solution</h3>

A) The oddball numbers give you a clue immediately that the value of house 1 will be best modeled by an exponential function.

The value of house 2 is increasing steadily at 9,000 per year, so is modeled by a linear function.

B) The ratio of values from a given year to the year before for house 1 is

... 294.58/286 = 1.03

A check for other years reveals the same ratio, so the exponential function can be written for house 1 as

... f(x) = 286·1.03^x . . . . . value of house 1

In part A we determined the year-to-year difference in value for house 2 is 9,000. That is the slope of the linear function. Then (in thousands), that function is

... f(x) = 286 +9x . . . . . value of house 2

C) After 25 years, the house values are (in thousands of dollars)

f_1(25)=286\cdot 1.03^{25}\approx 598.82049\\\\f_2(25)=286+9\cdot 25=511.00000

The value of house 1 has more than doubled in the same time that the value of house 2 has increased by about 79%. This is a significant difference.

___

An exponential function will always outperform a linear function over a long enough time period.

You might be interested in
Hannah placed 42,000
hammer [34]
Hannah.............. :)
3 0
3 years ago
Read 2 more answers
Which is the answer? :(
klio [65]

Answer:

the answer is :)

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
While testing a new vaccine, a lab technician noticed that the number of bacteria reduced by half every minute. How long does it
ANTONII [103]
As we know that 
x=x0*[1/2]n
putting the values 
375=3000*[1/2]n
375/3000=<span>[1/2]n
</span>1/8=<span>[1/2]n
simplify
[1/2]3=</span><span>[1/2]n
by cancelling them
so n=3
so it will take 3 minutes
hope it helps</span>
7 0
3 years ago
I need to find the equation of the line. Can someone please help?
NikAS [45]

The formula is y = mx + b when b = y-intercept and m is the slope.

Slope = Rise/Run So 1/2.

Y-Int. = The y value at which x = 0. Which is -3

The line has the formula:

Y = 1/2x - 3

Hope this helps :)

7 0
2 years ago
Read 2 more answers
What is the true solution to the logarithmic equation below?<br> log₂ (6x)-log₂ (√x)=2
slega [8]

Answer:

The true solution is x=4/9

EXPLANATION

The logarithmic equation given to us is

We need to use the quotient rule of logarithms.

When we apply this law the expression becomes

We now take the antilogarithm of both sides to get

We square both sides to get,

We evaluate to obtain,

This simplifies to

We divide both sides by 36 to get

We simplify to get,

6 0
2 years ago
Read 2 more answers
Other questions:
  • Given f(x) = - 3x - 2 and g(x) = - 2x - 4 , find h(x) = g(x) - f(x) .
    7·1 answer
  • Please help me thank you​
    15·1 answer
  • Portage Park is a perfect square. The length of each side of the park is 200 feet.
    12·2 answers
  • Evans has 32 hair ties Melanie has8 hair ties.what is the ratio?
    7·2 answers
  • What is the measure of angle D?<br><br> 52<br> 54<br> 57<br> 126
    13·2 answers
  • What is the slope? Show work as well please.
    6·1 answer
  • When a biased coin is thrown 4 times, the probability of getting 4 heads is
    11·1 answer
  • I have a pile of socks which contains 12 white socks, 12 black socks, and 12 red socks. How many socks must I take from the pile
    5·2 answers
  • What is 4.2 divided by 20.076
    5·1 answer
  • two positive integers have a product of 176. one integer is 5 less than the other integer. which equation can be used to find th
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!