Respuesta :
Answer:
y = 340e^0.0427276t ; 908
Step-by-step explanation:
Given that :
t = time in days since study began
Number of bacteria after 11 days = 544
y = number of bacteria at time t
Exponential growth model:
y = ae^rt
Where a = initial amount ; r = Growth rate
y = 544 ; t = 11 ; a = 340
544 = 340*e^11t
544/340 = e^11t
1.6 = e^11t
Take the In of both sides
In(1.6) = 11t
0.4700036 = 11t
t = 0.4700036 / 11
t = 0.0427276
y = 340e^0.0427276t
Number of bacteria after 23 days :
Using the formula above :
t = 23
y = 340e^0.0427276(23)
y = 340 * 2.6717529
y = 908.39600
y = 908
The required formula is [tex]y = 340e^{0.0427}[/tex]
908 bacteria are there 23 days after the beginning of the study .
Given that,
A certain culture of bacteria has a population of 340.
The population grows according to a continuous exponential growth model. After 11 days, there are 544 bacteria.
We have to find,
Write a formula relating y tot. Use exact expressions to fill in the missing parts of the formula.
How many bacteria are there 23 days after the beginning of the study.
According to the question,
- Let t be the time (in days) since the beginning of the study,
And let y be the number of bacteria at time,
t = time in days since study began
Number of bacteria after 11 days = 544
y = number of bacteria at time t
Then,
Exponential growth model:
[tex]y = a.e^{rt}[/tex]
Where, a = initial amount ; r = Growth rate
y = 544 ; t = 11 ; a = 340
Then,
[tex]544 = 340.e^{11t}\\\\\dfrac{544}{340} = e^{11t}\\\\1.6 = e^{11t}\\\\Taking \ log \ on \ both \ sides,\\\\ln(1.6) = 11t\\\\0.47 = 11t \\\\t = \dfrac{0.47}{11}\\\\t = 0.0427[/tex]
The required formula is [tex]y = 340e^{0.0427}[/tex]
- There 23 days after the beginning of the study Number of bacteria after 23 days :
[tex]y = 340e^{0.0427}[/tex]
Where, t = 23
[tex]y = 340e^{0.0427276(23)}\\\\y = 340 \times 2.6717529\\\\y = 908.39600\\\\y = 908[/tex]
Therefore, 908 bacteria are there 23 days after the beginning of the study .
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