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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)
Mathematics
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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Which equation represents a line with a slope of<br> 5/2and a y-intercept of -8/3
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Answer:

y=5/2x-8/3

Step-by-step explanation:

The equation is y=mx+b

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Which equation is the inverse of y = 9x2 - 4?
m_a_m_a [10]

Answer:

The inverse will be:

y' = \frac{\sqrt{x+4}}{3}

Step-by-step explanation:

In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :

f(x)  = 9x^{2} - 4

y = 9x^{2} - 4

x = 9y' ^{2} - 4

Now solve for y'.

First add 4 in both sides of the equation and change to the left y'.

x + 4= 9y'^{2} - 4+4

9y'^{2} = x + 4

Second divide by 9

9y'^{2}/9 = (x + 4)/9

y'^{2} = (x + 4)/9

Now you will have to clear y, with the square root.

[tex]y'^{\frac{2}{2}} = \sqrt{x + 4}  / \sqrt{9}[/tex] =

Simplifying terms

y' = \frac{\sqrt{x+4}}{3}

f^{-1}(x)  = \frac{\sqrt{x+4}}{3}

You can check the answer by doing the evaluation of the following equation:

(f o f^{-1} ) (x)

substitute the equation for y' or inverse function f^{-1}

f(\frac{\sqrt{x+4} }{3})

Now substitue the value into f(x)

You will have

= 9(\frac{\sqrt{x+4} }{3}} )^{2}  - 4\\\\Solving\\\\9(\frac{{x+4} }{9}} )  - 4

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5 0
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Given: The racer moves at 13.1 miles per hour expends energy at a rate of 645 calories per hour.

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Solution: We have,

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So, energy expended while moving 13.1 miles =645 calories.

Now, energy expended while moving 1 mile =\frac{645}{13.1} calories.

So, energy expended while moving 26.2 miles =\frac{645}{13.1}\times 26.2=645\times 2=1290 calories.

Hence, 1290 calories of energy is required to complete a marathon race 26.2 miles at this pace.

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