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3 years ago

. City workers recorded the number of squirrels in a park over a period of time. At the first count, there were 15 pairs

Mathematics

1 answer:

coldgirl [10]3 years ago

3 0

Answer:

Exponential

P(X) = P_0 (2)^{2x}

Step-by-step explanation:

Given that at the first count, there were 15 pairs

of male and female squirrels (30 squirrels total). After 6 months, the city workers recorded a total of 60 squirrels,

and after a year, there were 120.

i.e. every 6 months population of squirrel is doubling.

a) Function is exponential since every time of 6 months population is doubled

b) The function that represents the population of squirrels recorded over x number of years.

We know that every 1/2 year it doubles. Hence initially if P0 is started with in 1/2 year it would be 2P0 and in 1 year it would be 4P0 and so on.

In other words, the model would be

$P(X) = P_0 (2)^{2x}$ where x = no of years

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Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.

Inessa [10]

To model this situation we are going to use the exponential decay function: $f(t)=a(1-b)^t$
where
$f(t)$ is the final amount remaining after $t$ years of decay
$a$ is the initial amount
$b$ is the decay rate in decimal form
$t$ is the time in years

For substance A:
Since we have 300 grams of the substance, $a=300$ . To convert the decay rate to decimal form, we are going to divide the rate by 100%:
$r= \frac{0.15}{100} =0.0015$ . Replacing the values in our function:
$f(t)=a(1-b)^t$
$f(t)=300(1-0.0015)^t$
$f(t)=300(0.9985)^t$ equation (1)

For substance B:
Since we have 500 grams of the substance, $a=500$ . To convert the decay rate to decimal form, we are going to divide the rate by 100%:
$r= \frac{0.37}{100} =0.0037$ . Replacing the values in our function:
$f(t)=a(1-b)^t$
$f(t)=500(1-0.0037)^t$
$f(t)=500(0.9963)^t$ equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass $M$ , we can replace $f(t)$ with $M$ in both equations:
$M=300(0.9985)^t$ equation (1)
$M=500(0.9963)^t$ equation (2)

We can conclude that the system of equations that can be used to determine <span>how long it will be before the substances have an equal mass, </span> $M$ , is:
$\left \{ {{M=300(0.9985)^t} \atop {M=500(0.9963)^t}} \right.$

Solving the system, we can show that it will take approximately 231.59 years for that to happen.

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3 years ago

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An office building rents for $40,000 the first year, then increases by 0.5% each year. Use summation notation to represent the t

Sholpan [36]

Given the initial rent is $40000, and the rent is increased by 0.5% each year, the rent in the third year will be given by:
FV=P(1+r)^n
FV=40000(1.05)^n
Thus the answer for the sum of payments for 3 years will be:
The summation is 1.05 raised to n years times $40000, where the years is from 0 to 3.

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You work at a restaurant as a host and a server. You earn $9.45 for each hour you work as a host and $7.65 for each hour you wor

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9.45x + 7.65y = 160.65

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3 years ago

A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required

Katyanochek1 [597]

Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

The estimate is of $\pi = 0.61$ , while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}$

$0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}$

$\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2$

$n = 1015.5$

Rounding up, 1016 constituents are required.

More can be learned about the z-distribution at brainly.com/question/25890103

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