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Radda [10]
3 years ago
10

On the basis of data collected during an experiment, a biologist found that the growth of a fruit fly population (Drosophila) wi

th a limited food supply could be approximated by
N(t) = 600/1+39e^-0.16t
(a) What was the initial fruit fly population in the experiment? where t denotes the number of days since the beginning of the experiment.
(b) What was the population of the fruit fly colony on the t = 11 day? (Round your answer to the nearest integer.)
Mathematics
1 answer:
Ket [755]3 years ago
3 0

Answer:

(a). 15

(b). 78

Step-by-step explanation:

Growth of the population of a fruit fly is modeled by

N(t) = \frac{600}{1+39e^{-0.16t} }

where t = number of days from the beginning of the experiment.

(a). For t = 0 [Initial population]

N(0) = \frac{600}{1+39e^{-0.16\times 0} }

       = \frac{600}{1+39}

       = \frac{600}{40}

       = 15

Initial population of the fruit flies were 15.

(b).Population of the fruit fly colony on 11th day.

N(11) = \frac{600}{1+39e^{-0.16\times 11} }

       = \frac{600}{1+39e^{-1.76} }

       = \frac{600}{1+39\times 0.172 }

       = \frac{600}{1+6.71}

       = \frac{600}{7.71}

       = 77.82

       ≈ 78

On 11th day number of fruit flies colony were 78.

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The approximate temperature of the pan after it has been away from the heat for 9 minutes is 275.59°F.

Step-by-step explanation:

The formula for D, the difference in temperature between the pan and the room after t minutes is:

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Compute the approximate difference in temperature between the pan and the room after 9 minutes as follows:

D = 324\cdot e^{-0.05t}

    =324\times e^{-0.05\times 9}\\\\=206.59

Then the approximate temperature of the pan after it has been away from the heat for 9 minutes is:

D = P - R

206.59 = P - 69

P = 206.59 + 69

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When finding the sum of 512 and –614, Josh used a left-to-right algorithm to compute the answer. He first added the hundred’s di
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Answer:

<em>Yes, Josh's answer</em><em> is </em><em>correct</em><em> as </em><em> –102</em><em>  is the correct answer.</em>

<em>Josh have computed the sum as:</em>

<em>If the two integers having different signs, we need to subtract the absolute values (the digits without signs) and then just make sure to keep the sign of the number with the larger absolute value.</em>

     − 6 1 4

+    + 5 1 2

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     - 1 0 2

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Staring from right, − 614 + (+512) = -102 can be obtained by first adding 2 in negative 4, then adding 1 in negative 1, and lastly adding 5 in negative 6.

Ultimately we can say that Negative 614 plus Positive 514 equals Negative 102.

So, the sum of 512 and –614 is  -102 i.e − 614 + (+512) = -102

Step-by-step explanation:

This is how Josh used a left-to-right algorithm to compute the answer:

  1. Adding the hundred’s digits 500 + (–600) = –100
  2. Adding the ten's digits 10 + (–10) = 0
  3. Lastly, adding 2 + (–4) = –2
  4. End result –100 + 0 + (–2) = –102

<em>Yes, Josh's answer is correct. </em>

<em>How else could Josh have computed the sum?</em>

Before mentioning how Josh could have computed the sum. Here are some of the facts about sum of numbers:

  • The sum of two negative integers is a negative integer. For example,

Adding two negative integers: -3 and -5

-3 + -5 = -8

Please, you don't need to confuse the sign or symbol of the integer with the operation being performed.

Just note -3 + -5 = -8 which is read as is read as Negative 3 plus negative 5 equals negative 8.

  • The sum of two positive integers is a positive integer.

Adding two positive integers: ⁺3 and ⁺5

(⁺3) + (⁺5) = ⁺8

Please, you don't need to confuse the sign or symbol of the integer with the operation being performed.

Just note ⁺3 + ⁺5 = ⁺8 which is read as is read as Positive 3 plus positive 5 equals positive 8.

  • To add a positive and a negative integer

As +(+) are like signs, so they become a positive sign. Such as:

−5 + (+ 1) = −5 + 1 = -4

As

+ + ⇒ +  

+ − ⇒ −  

− + ⇒ −

− − ⇒ +

<em>If the two integers having different signs, we need to subtract the absolute values (the digits without signs) and then just make sure to keep the sign of the number with the larger absolute value.</em>

So, What is −614 + (+512)?

       

     − 6 1 4

+    + 5 1 2

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     - 1 0 2

_________

Staring from right, − 614 + (+512) = -102 can be obtained by first adding 2 in negative 4, then adding 1 in negative 1, and lastly adding 5 in negative 6.

Ultimately we can say that Negative 614 plus Positive 514 equals Negative 102.

<em>So, the sum of 512 and –614 is  -102 i.e − 614 + (+512) = -102</em>

<em>Keywords: integer, sum, numbers, digit</em>

<em>Learn more about sum of integers from brainly.com/question/591533</em>

#learnwithBrainly

3 0
3 years ago
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