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2 years ago

What is the logarithmic formula 10000= 625/8*2^t ?

Mathematics

1 answer:

Elodia [21]2 years ago

8 0

9514 1404 393

Answer:

log(128) = t·log(2)

Step-by-step explanation:

You can take logarithms the way the formula is, or you can simplify it first.

As is

log(10000) = log(625) -log(8) +t·log(2)

Simplified

8·10000/625 = 2^t . . . . . multiply by 8/625

128 = 2^t

log(128) = t·log(2)

_____

Solution:

t = log(128)/log(2) = 7

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The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

Anettt [7]

Answer:

1) The size of the colony after 4 days is 6553 mosquitoes

2) After $t = 4.9\ days$

Step-by-step explanation:

To answer this question you must use the growth formula

$N = N_0e ^ {kt}$

Where

$N_0$ is the initial population of mosquitoes = 1000

t is the time in days

k is the growth rate

N is the population according to the number of days

We know that when t = 1 and $N_0=1000$ then N = 1600

Then we use these values to find k.

$1600 = 1000e ^{k(1)}\\\\\frac{1600}{1000} = e ^ k\\\\ln(\frac{1600}{1000}) = k\\\\k = 0.47$

Now that we know k we can find the size of the colony after 4 days.

$N = 1000e ^ {0.47(4)}\\\\N = 6553\ mosquitoes$

To know how long it should take for the population to reach 10,000 mosquitoes we must do N = 10000 and solve for t.

$10000 = 1000e ^ {0.47t}\\\\10 = e ^ {0.47t}\\\\ln(10) = 0.47t\\\\t = \frac{ln(10)}{0.47}\\\\t = 4.9\ days$

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2 years ago

Why is 15 + 1/2 an algebraic expression?

Marat540 [252]

Answer:

There is no equal sign.

Step-by-step explanation:

There is no equal sign to make it an algebraic equation.

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2 years ago

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Find the four rational numbers and irrational numbers between 2/5 and 5/6

Savatey [412]

The four?

Of course there are an infinite number of rationals between any two different real numbers, as well as an even bigger infinite number of irrationals.

The average will be between the numbers:

$\frac 1 2 (\frac 2 5 + \frac 5 6) = \dfrac{37}{60}$

That's a lot of work to get a number in between. We can just see

$\frac 1 2$
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The mediant, or freshman addition, will always be in between:

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2/5=.4 and 5/6 is about .83, so

$.6 = \frac{6}{10}$

is in between as is .7, .41, .530940394 and as many rationals as we care to generate.

To get irrationals we could just add a teeny irrational to the ones we just generated, like $\frac{6}{10} + \frac{\pi}{100}$

We could just change that denominator a bit and get as many as we like.

But let's get some square roots. The geometric mean will be between

$\sqrt{ \dfrac 2 5 \cdot \dfrac 5 6 } = \dfrac{1}{\sqrt{3}}
$

That's the tangent from one of trig's biggest cliches, but I digress. It's in between.

While we're on trig cliches,

$\dfrac{1}{\sqrt{2}}$

is in between as well.

Keeping with the trig theme, also in between are

$\dfrac{\pi} 6$

and

$\dfrac{\pi}{4}$

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We could obviously go on as long as we cared to.

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3 years ago

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the exact answer is 3 over
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Honi maded the mistake in step 1

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