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3 years ago

How do linear and exponential functions compare over time?

Mathematics

1 answer:

Murljashka [212]3 years ago

8 0

Answer:

Exponential Functions

In linear functions, rate of change is constant: as x goes up, y will go up a consistent amount. In exponential functions, the rate of change increases by a consistent multiplier—it will never be the same, but there will be a pattern.

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Suppose that commercial airplane crashes in a certain country occur at the rate of 2.5 per year. what is the probability that fo

lesya [120]

The poisson distribution applies here.
$\lambda=2.5$
$P(X=4)=\frac{e^{-2.5}\times2.5^{4}}{4!}=0.134$

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3 years ago

A line with (5,6) and a slope of 2/15

BlackZzzverrR [31]

Slope, shmlope. What's the q?

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4 years ago

The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial

qaws [65]

Answer:

Step-by-step explanation:

Let P be the population of the community

So the population of a community increase at a rate proportional to the number of people present at a time

That is

$\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0$

Solve this equation we get

$p(t)=p_0e^{kt}---(1)$

where p is the present population

p₀ is the initial population

If the initial population as doubled in 5 years

that is time t = 5 years

We get

$2p_o=p_oe^{5k}\\\\e^{5k}=2$

Apply In on both side to get

$Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}$

Substitute $k=\frac{In2}{5}$ in $p(t)=p_oe^{kt}$ to get

$\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}$

Given that population of a community is 9000 at 3 years

substitute t = 3 in ${p(t)=p_oe^{\frac{In2}{5}t }}$

$p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8$

<h3>Therefore, the initial population is 5937.8</h3>

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3 years ago

How many times as great as the value of the digit 3 in 47,235 is the value of the digit 3 in 2,438,017

pashok25 [27]

Answer:

$10^{3}$ times

Step-by-step explanation:

The value of 3 in 47,235 is 30 (ignoring the number that follows, 5)

The value of 3 in 2,438,017 is 30,000 (ignoring the numbers that follow)

The value of digit 3 in 2,438,017 is $\frac{30,000}{30}$ = $10^{3}$ times greater than the value of 3 in 47,235

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4 years ago

A curtain machine must be between 2.73 and 3.55 inches which is greater than 2.73 and 3.55

Vladimir79 [104]

3.55 because three is greater than two

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3 years ago

Read 2 more answers