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11 et 12

The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

Kategorie: statistics Aktualisiert: 2026-02-08

Aufgabe

Turn 1 Question
  1. a bacterial culture initially contains 250 bacteria. find the rule of the function that associates, to the time, in hours, elapsed since the beginning, the number of bacteria, if the number of bacteria: a) doubles every 2 hours; b) increases by 25% every 10 minutes; c) decreases by 4% every half - hour; d) triples every day. 10. the number of bacteria in a culture doubles every 20 minutes. how many bacteria were there initially if we observe 20480 bacteria after 4 hours of observation? 11. a grocery basket costs $240 in 2014. if we predict that the cost of this basket will be $269.97 in 2017, what was the annual inflation rate during those three years? 12. they are 140 occupied residences in a building complex. it is expected that this number will increase at a certain rate every 2 years. if after 6 years, there are 197 occupied residences, what is the expected increase rate?
Turn 2 Question

11 et 12

Lösungsschritte

  1. Understand the question
    Turn 1 Question
    1. a bacterial culture initially contains 250 bacteria. find the rule of the function that associates, to the time, in hours, elapsed since the beginning, the number of bacteria, if the number of bacteria: a) doubles every 2 hours; b) increases by 25% every 10 minutes; c) decreases by 4% every half - hour; d) triples every day. 10. the number of bacteria in a culture doubles every 20 minutes. how many bacteria were there initially if we observe 20480 bacteria after 4 hours of observation? 11. a grocery basket costs $240 in 2014. if we predict that the cost of this basket will be $269.97 in 2017, what was the annual inflation rate during those three years? 12. they are 140 occupied residences in a building complex. it is expected that this number will increase at a certain rate every 2 years. if after 6 years, there are 197 occupied residences, what is the expected increase rate?
    Turn 2 Question

    11 et 12

  2. Response
    Turn 1 Answer

    Let's solve question 10: "The number of bacteria in a culture doubles every 20 minutes. How many bacteria were there initially if we observe 20 480 bacteria after 4 hours of observation?"

  3. Explanation

    Step 1: Determine the number of periods

    First, we need to find how many 20 - minute periods are in 4 hours. Since 1 hour = 60 minutes, 4 hours = 4×60 = 240 minutes. The number of 20 - minute periods \( n=\frac{240}{20}=12 \).

    Step 2: Use the exponential growth formula

    The formula for exponential growth when the quantity doubles is \( y = a\times2^{n} \), where \( y \) is the final quantity, \( a \) is the initial quantity, and \( n \) is the number of doubling periods. We know that \( y = 20480 \) and \( n = 12 \). We need to solve for \( a \).

    From \( y=a\times2^{n} \), we can re - arrange the formula to \( a=\frac{y}{2^{n}} \).

    Substitute \( y = 20480 \) and \( n = 12 \) into the formula: \( 2^{12}=4096 \), so \( a=\frac{20480}{4096}=5 \).

  4. Final answer

    The initial number of bacteria is 5.

    Turn 2 Answer

    Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières.

    Pour le numéro 11, on cherche le taux d'inflation annuel.

    1. Le prix passe de 240 $ à 269,97 $ sur 3 ans (de 2014 à 2017).
    2. La formule c'est : $269,97 = 240(1 + i)^3$.
    3. En isolant, on a $(1 + i)^3 = \frac{269,97}{240} \approx 1,124875$.
    4. Pour trouver $1 + i$, on fait la racine cubique : $\sqrt[3]{1,124875} \approx 1,04$.
    5. Donc le taux $i$ est de 4 %. (On dirait que c'est ce que tu as écrit au crayon, bien joué !)

    Pour le numéro 12, c'est le même principe avec les résidences :

    1. On passe de 140 à 197 résidences en 6 ans. Comme le taux s'applique "tous les 2 ans", il y a 3 périodes de 2 ans ($6 \div 2 = 3$).
    2. L'équation est : $197 = 140(1 + r)^3$.
    3. On divise : $(1 + r)^3 = \frac{197}{140} \approx 1,407$.
    4. On prend la racine cubique : $1 + r = \sqrt[3]{1,407} \approx 1,1205$.
    5. Le taux d'augmentation est donc d'environ 12,05 % tous les 2 ans.

    C'est pas mal de calculs de racines tout ça, tu t'en sors avec ta calculatrice ?

Antwort

Response

Turn 1 Answer

Let's solve question 10: "The number of bacteria in a culture doubles every 20 minutes. How many bacteria were there initially if we observe 20 480 bacteria after 4 hours of observation?"

Explanation

Step 1: Determine the number of periods

First, we need to find how many 20 - minute periods are in 4 hours. Since 1 hour = 60 minutes, 4 hours = 4×60 = 240 minutes. The number of 20 - minute periods \( n=\frac{240}{20}=12 \).

Step 2: Use the exponential growth formula

The formula for exponential growth when the quantity doubles is \( y = a\times2^{n} \), where \( y \) is the final quantity, \( a \) is the initial quantity, and \( n \) is the number of doubling periods. We know that \( y = 20480 \) and \( n = 12 \). We need to solve for \( a \).

From \( y=a\times2^{n} \), we can re - arrange the formula to \( a=\frac{y}{2^{n}} \).

Substitute \( y = 20480 \) and \( n = 12 \) into the formula: \( 2^{12}=4096 \), so \( a=\frac{20480}{4096}=5 \).

Answer

The initial number of bacteria is 5.

Turn 2 Answer

Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières.

Pour le numéro 11, on cherche le taux d'inflation annuel.

  1. Le prix passe de 240 $ à 269,97 $ sur 3 ans (de 2014 à 2017).
  2. La formule c'est : $269,97 = 240(1 + i)^3$.
  3. En isolant, on a $(1 + i)^3 = \frac{269,97}{240} \approx 1,124875$.
  4. Pour trouver $1 + i$, on fait la racine cubique : $\sqrt[3]{1,124875} \approx 1,04$.
  5. Donc le taux $i$ est de 4 %. (On dirait que c'est ce que tu as écrit au crayon, bien joué !)

Pour le numéro 12, c'est le même principe avec les résidences :

  1. On passe de 140 à 197 résidences en 6 ans. Comme le taux s'applique "tous les 2 ans", il y a 3 périodes de 2 ans ($6 \div 2 = 3$).
  2. L'équation est : $197 = 140(1 + r)^3$.
  3. On divise : $(1 + r)^3 = \frac{197}{140} \approx 1,407$.
  4. On prend la racine cubique : $1 + r = \sqrt[3]{1,407} \approx 1,1205$.
  5. Le taux d'augmentation est donc d'environ 12,05 % tous les 2 ans.

C'est pas mal de calculs de racines tout ça, tu t'en sors avec ta calculatrice ?

Question Analysis

Subject mathematics
Sub Subject statistics
Education Level high school
Difficulty unspecified
Question Type calculation
Multi Question Yes
Question Count 2
Analysis Status completed
Analyzed At 2026-02-08T20:47:20

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Show OCR extraction 
11 et 12

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