Mathematics, 25.01.2021 20:30 SmokeyRN

At the beginning of a study, 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. (a) Lett be the time (in days) since the beginning of the study, and let y be the number of bacteria at time i. x 5 ? Write a formula relating y tot. Use exact expressions to fill in the missing parts of the formula. Do not use approximations.
y = 10:
(b) How many bacteria are there 23 days after the beginning of the study? Do not round any intermediate computations, and round your answer to the nearest whole number.
bacteria

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Answer from: natalie857123

The required formula is $y = 340e^{0.0427}$

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:

$y = a.e^{rt}$

Where, a = initial amount ; r = Growth rate

y = 544 ; t = 11 ; a = 340

Then,

$544 = 340.e^{11t}\\\\\dfrac{544}{340} = e^{11t}\\\\1.6 = e^{11t}\\\\Taking \ log \ on \ both \ sides,\\\\ln(1.6) = 11t\\\\0.47 = 11t \\\\t = \dfrac{0.47}{11}\\\\t = 0.0427$

The required formula is $y = 340e^{0.0427}$

There 23 days after the beginning of the study Number of bacteria after 23 days :

$y = 340e^{0.0427}$

Where, t = 23

$y = 340e^{0.0427276(23)}\\\\y = 340 \times 2.6717529\\\\y = 908.39600\\\\y = 908$

Therefore, 908 bacteria are there 23 days after the beginning of the study .

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Answer from: miguelsanchez1456

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

Answer from: Quest

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

$m\angle qrt=156^o$

$m\angle qst=156^o$

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

Answer from: Quest

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.

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At the beginning of a study, a certain culture of bacteria has a population of 340. The population g...