How to write the equation in standard form

The populations of termites and spiders in a certain house are growing exponentially. The house contains 120 termites the day yo

zysi [14]

Answer:

in order to triple the inicial population of spiders, will take 50395 days

Step-by-step explanation:

we can define the termite population function as T(t) and the one for spiders as S(t) , where t represents time measured in days

since both have and exponencial growth

T(t)= a*e^(b*t)

S(t)= c*e^(d*t)

1) when the day the person moves in , t=0 and T(0)= 120 termites

T(0) = a*e^(b*0) = a = 120

2) after 4 days , t=4 and the house contains T(4) = 210 termites

T(4)= 120*e^(b*4) = 210 → 4*b = ln (210/120) → b = (1/4)* ln(210/120)= 0.14

therefore

T(t) = 120*e^(0.14*t)

3) 3 days after moving in , t=3, there were T(3) = 120*e^(0.14*3)=182.63≈ 182 termites . The number of spiders is half of the number of termites → S(3) = T(3) * 1 spider/ 2 termites =91.31 spiders ≈ 91 spiders

4) after 8 days of moving in , t=8, there were T(8) = 120*e^(0.14*8)=367.78≈ 368 termites . The number of spiders is 0.25 times the number of termites → S(8) = T(8) * 1 spider/ 4 termites =91.94 spiders ≈ 92 spiders

from

S(t)= c*e^(d*t) → d = ln [S (tb)/S (ta) ] / (tb-ta)

therefore d = ln [ S(8)/S(3) ] / (8 - 3 ) = 2.18*10^-5

in order to triple the initial population

S(t3) = 3 *S(0) = 3*[c*e^(d*0)] = 3*c

S(t3) = c*e^(d*t3) = 3* c → t3 = ln(3) / d = 50395 days

5 0

3 years ago

Pencils cost 25p each. Mr smith spends £15 on pencils. Work out the number of pencils he gets.

marshall27 [118]

Answer:

Step-by-step explanation:

7 0

3 years ago

Rectangle ABCD is translated (x + 2 y - 3) and then rotated 180° about the origin. Complete the table to show the locations of A

katen-ka-za [31]

Answer:

A

Step-by-step explanation:

4 0

2 years ago

Reports on a student’s ACT, SAT, or MCAT usually give the percentile as well as the actual score. The percentile is just the cum

DaniilM [7]

Answer:

The percentile is calculated with the following probability:

$P(X$

And using the z score we got:

$P(X$

So then we can conclude that 31 represent approximately the percentile 81 on the distribution given

He scored better than about 80.98 % of all MCAT takers.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(25.3,6.5)$

Where $\mu=25.3$ and $\sigma=6.5$

And for this case we have a score of 31

The percentile is calculated with the following probability:

$P(X$

And using the z score we got:

$P(X$

So then we can conclude that 31 represent approximately the percentile 81 on the distribution given

He scored better than about 80.98 % of all MCAT takers.

6 0

2 years ago

Students in a class were asked to name their favorite sport they like to watch on television. How many more time students want t

levacccp [35]

First, we need to add up all the percentages to make sure we have 100%.

25.5% + 0.03% = 25.53%

This means that 74.47% of the students chose something other than basketball or soccer.

The amount of students you stated there were was 2553.

25.5% of 2553 is 651 students and

0.03% is 8 students.

Now, we divide 651 by 8 to determine the amount of times over basketball was chosen.

651 ÷ 8 = 81

Basketball was chosen 81 times over again compared to soccer.

To find how much more times basketball was chosen, subtract 8 from 651

651 - 8 = 643

Basketball was chosen 643 times more than soccer.

8 0

3 years ago

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