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Vladimir79 [104]

3 years ago

5

The population of a certain single-cell organism doubles every hour, starting with 100 cells. Which COULD be an equation to mode

l this situation, where f(t) is the number of organisms and t is time in hours?
A) f(t) = 200t
B) f(t) = 100(2t)
C) f(t) = 2t + 100
D) f(t) = 100(1/2t)

1 answer:

aivan3 [116]3 years ago

4 0

none of the answers are correct

f(t) = 100 x 2^t

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consider the function and then use calculus to answer the questions that follow 1 1/x 5/x^2 1/x^3 (a) Find the interval(s) where

boyakko [2]

Answer:

a) $X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)$

b) $Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0 )$

Step-by-step explanation:

From the question we are told that

The Function

$f(x)=1+\frac{1}{x} +\frac{5}{x^2} +\frac{1}{x^3}$

Generally the differentiation of function f(x) is mathematically solved as

$f(x)=1+\frac{1}{x} +\frac{5}{x^2} +\frac{1}{x^3}$

$f(x)=\frac{x^3+x^2+5x+1}{x^2}$

Therefore

$f'(x)=\frac{x^2+10x+3}{x^4}$

Generally critical point is given as

$f'(x)=0$

$\frac{x^2+10x+3}{x^4}=0$

$x=-5 \pm\sqrt{22}$

Generally the maximum and minimum x value for critical point is mathematically solved as

$f'(-5 \pm\sqrt{22})$

Where

Maximum value of x

$f'(-5 +\sqrt{22})$

Minimum value of x

$f'(-5 +\sqrt{22})$

Therefore interval of increase is mathematically given by

$f'(-5 -\sqrt{22}),f'(-5 +\sqrt{22})$

$f(x)$

Therefore interval of decrease is mathematically given by

$(-\infty,-5 -\sqrt{22}),f'(-5 +\sqrt{22},0),(0,\infty)$

Generally the second differentiation of function f(x) is mathematically solved as

$f''(x)=\frac{2(x^2+15x+6)}{x^5}$

Generally the point of inflection is mathematically solved as

$f''(x)=0$

$x^2+15x+6=0$

Therefore inflection points is given as

$x=\frac{1}{2} (-15 \pm \sqrt{201}$

$f''(x)>0,\frac{1}{2}(-15-\sqrt{201})$

a)Generally the concave upward interval X is mathematically given as

$X=((-15-\sqrt{201},(-15+\sqrt{201}),(0,\infty)$

$f''(x)$

b)Generally the concave downward interval Y is mathematically given as

$Y=(\infty,\frac{1}{2}(-15-\sqrt{201} ) ),(\frac{1}{2}()-15+\sqrt{201)},0 )$

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Casey has been running for 3 days

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Mike collected milk from 3 of his cows at the dairy farm. from the first cow, he collected 4/5 gallon of milk. the second cow pr

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Answer:

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(B) 1 7/15

Step-by-step explanation:

(A) Add the gallons he collected together to get the total amount of milk he started with: 4/5 + 6/8 + 3/4 = 2 3/10 gallons of milk.

(B) Take that number, 2 3/10, and subtract the amount of milk he has left to get the amount of milk he used. 2 3/10 - 5/6 = 1 7/15

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3 years ago

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aleksklad [387]

Correct answer: 1) (f/g)(x)

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3 0

1 year ago

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8_murik_8 [283]

Answer:

2

Step-by-step explanation:

The average rate of change over [2, 8] is the change in the y-values over the change in the x-values.

$\frac{f(8) - f(2)}{8 - 2}$

$f(8) = 2(8) - 8 = 16 - 8 = 8$

$f(2) = 2(2) - 8 = 4 - 8 = -4$

$\frac{8 - (-4)}{8-2} = \frac{8 + 4}{8-2} = \frac{12}{6} = 2$

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3 years ago