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4 years ago

50 POINTS!!! WILL GIVE BRAINLIEST!!!

Mathematics

1 answer:

lorasvet [3.4K]4 years ago

5 0

<h3>Given</h3>

The values of two houses (in thousands of dollars)

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

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.

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3 years ago

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Answer:

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Number of spectators who leave the stadium before 180 minutes

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The data can be collected via the exit time entries at the exit gate of the stadium

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<u>how to apply the data</u>

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3 years ago

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4 years ago

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

50 POINTS!!! WILL GIVE BRAINLIEST!!!