Mathematics, 26.12.2019 04:31 haileyglowiak8183

Aresearch student is working with a culture of bacteria that doubles in size every twenty minutes. the initial population count was 1350 bacteria. rounding to five significant digits, write an exponential equation representing this situation. to the nearest whole number, what is the population size after 3 hours?

Answers: 3

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Answer from: bnbjj

p(t) = 1350·2^(t/20); p(180) = 691,200p(t) ≈ 1350·e^(0.034657t); p(180) ≈ 691,155

Step-by-step explanation:

The situation can be represented exactly by the exponential equation ...

p = 1350·2^(t/20) . . . . . . t in minutes; p is population count

After 3 hours (180 minutes), the population is ...

p = 1350·2^(180/20) = 1350·2^9 = 691,200 . . . population after 3 hours

Alternate Solution

Some prefer their exponential functions to be in the form ...

p = a·e^(kt)

where "a" is the initial population count, and k is determined by the growth rate.

We can rewrite the two forms to allow us to match the various constants:

p = 1350·(2^(1/20))^t = a·(e^k)^t

This shows us that a=1350 and e^k = 2^(1/20). Then k = ln(2)/20 ≈ 0.034657

Now, the exponential function can be written as ...

p = 1350·e^(0.034657t)

Filling in t=180 in this equation, we find ...

p = 1350·e^(0.034657·180) ≈ 1350·511.967 ≈ 691,155.33 ≈ 691,155

Comment on the answers

My personal preference is for the exact form of the equation and the integer answer. I suppose your grader is expecting the second answer, since you were asked to round the equation to 5 significant digits, and to round the population to the nearest integer.

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

table 3 represents a direct variation function. : )

Which table represents a direct variation function?

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