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kicyunya [14]
3 years ago
8

URGENT, HELP ASAP

Mathematics
1 answer:
Ilya [14]3 years ago
4 0

Answer:

The sales will surpass 37 million in about 2013.

Step-by-step explanation:

The answer can be found via solving an exponential inequality as follows:

f(x) = 20(1.05)^x\\20(1.05)^x> 37\\1.05^x> \frac{37}{20}\\x\log 1.05>\log\frac{37}{20}=\log 37 - \log 20\\x>(\log 37 - \log 20)/\log 1.05=12.6\\x>12.6 \,\,\mbox{years}

Any number of years larger than 12.6 will satisfy the inequality, i.e., after more than 12.6 years from year 2000, the annual sales will surpass 37 million. The answer to the exact question will then be: in about 2013 the sales will surpass 37 million.

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Answer:

see below

Step-by-step explanation:

The equation for half life is

n = no  e ^ (-kt)

Where no is the initial amount of a substance , k is the constant of decay and t is the time

no = 9.8

1/2 of that amount is 4.9 so n = 4.9 and t = 100 years

4.9 = 9.8 e^ (-k 100)

Divide each side by 9.8

1/2 = e ^ -100k

Take the natural log of each side

ln(1/2) = ln(e^(-100k))

ln(1/2) = -100k

Divide each side by -100

-ln(.5)/100 = k

Our equation in years is

n = 9.8  e ^ (ln.5)/100 t)

Approximating ln(.5)/100 =-.006931472

n = 9.8 e^(-.006931472 t)  when t is in years

Now changing to days

100 years = 100*365 days/year

36500 days

Substituting this in for t

4.9 = 9.8 e^ (-k 36500)

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Divide each side by -100

-ln(.5)/36500 = k

Our equation in years is

n = 9.8  e ^ (ln.5)/36500 d)

Approximating ln(.5)/365=-.00001899

n = 9.8 e^(-.00001899 d)  when d is in days

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