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2 years ago

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Simplify x^10/x^8 I am writing this cause I need more charectars

2 answers:

FromTheMoon [43]2 years ago

8 0

The rule for division of similar bases with exponents:

(a^b)/(a^c)=a^(b-c)

In this case we have:

(x^10)/(x^8)

x^(10-8)

x^2

Juliette [100K]2 years ago

3 0

It's x^2. When dividing, just subtract the exponents

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A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is

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Answer:

$P(t) = 100e^{0.0251t}$

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

$P(t) = P(0)e^{kt}$

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that $P(0) = 100$ . So

$P(t) = 100e^{kt}$

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that $P(60) = 450$ , and we use this to find k. So

$450 = 100e^{60k}$

$e^{60k} = 4.5$

$\ln{e^{60k}} = \ln{4.5}$

$60k = \ln{4.5}$

$k = \frac{\ln{4.5}}{60}$

$k = 0.0251$

So

$P(t) = 100e^{0.0251t}$

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

$200 = 100e^{0.0251t}$

$e^{0.0251t} = 2$

$\ln{e^{0.0251t}} = \ln{2}$

$0.0251t = \ln{2}$

$t = \frac{\ln{2}}{0.0251}$

$t = 27.65$

The doubling time is of 27.65 minutes.

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Answer:

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A sketch of this situation can be seen below.

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2 years ago

For the graphed function f(x) = (4)x − 1 + 2, calculate the average rate of change from x = 1 to x = 2.

lorasvet [3.4K]

Average rate of the function: 3

Step-by-step explanation:

The function in this problem is

$f(x)=4^{x-1}+2$

The average rate of change of a function over an interval $(x_1,x_2)$ is given by

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where

$f(x_1),f(x_2)$ are the values of the function calculated in $x_1,x_2$ respectively

For the function in this problem we have:

$x_1=1$ , so

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So, the average rate of change is

$r=\frac{6-3}{2-1}=\frac{3}{1}=3$

Learn more about rate of change:

brainly.com/question/4152194

brainly.com/question/12941985

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2 years ago