Ask question

Ask question

All categories

3 years ago

8

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How many milligrams

of caffeine will be in your system after 8 hours? Round to two decimal places? Can someone show me how to work this problem out?

1 answer:

valentina_108 [34]3 years ago

8 0

Answer:

43.16 mg

Step-by-step explanation:

After each hour, the amount remaining is 100% - 12% = 0.88 times the amount present at the beginning of the hour. Then after 8 hours, the amount remaining will be the initial amount multiplied by 0.88 eight times, or ...

(120 mg)·(0.88^8) ≈ 43.1561 mg ≈ 43.16 mg

_____

Of course, an exponent is used to signify repeated multiplication. You can actually do the multiplication if you like, but most scientific and graphing calculators handle exponentiation easily.

You might be interested in

Find the sum of the first 25 terms in this geometric series:<br> 8 + 6 + 4.5...

Ksivusya [100]

Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{3}{4}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=8$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=8\left(\frac{3}{4}\right)^{n-1}$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}$

$=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}$

$=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32$

$=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}$

$=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}$ ∵ $\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}$

$=32\cdot \frac{4^{25}-3^{25}}{4^{25}}$

$=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}$

$=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}$ ∵ $\mathrm{Factor}\:32:\ 2^5$ , $\mathrm{Factor}\:4^{25}:\ 2^{50}$

so

$=\frac{4^{25}-3^{25}}{2^{45}}$ ∵ $\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}$

$=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}$

$=32-\frac{3^{25}}{2^{45}}$ ∵ $\frac{4^{25}}{2^{45}}=32$

$=32-0.024$ ∵ $\frac{3^{25}}{2^{45}}=0.024$

$=31.98$

Therefore, the sum of the first 25 terms in this geometric series: 31.98

3 0

3 years ago

Linda needs 20 gallons of juice that has 75%fruit juice. she has a mixture that has 80% fruit juice and another mixtures that ha

suter [353]

Linda should use ...
15 gallons of 80% juice
5 gallons of 60% juice

_____
Let g represent the number of gallons of 80% juice needed. Then (20-g) is the number of gallons of 60% juice Linda will use. The amount of juice in the mixture can be written as
0.80g +0.60(20 -g) = 0.75×20
0.20g = 20(0.75 -0.60) = 20×0.15
g = 20×0.15/0.20 = 15
The amount of 80% juice needed is 15 gallons, so 5 gallons of 60% juice are needed.

5 0

3 years ago

Subtract (r - 3q + 5p) - (-4r - 3q - 8p)

Alex787 [66]

Answer: ok so Let's simplify step-by-step.

r−3q+5p−(−4r−3q−8p)

Distribute the Negative Sign:

=r−3q+5p+−1(−4r−3q−8p)

=r+−3q+5p+−1(−4r)+−1(−3q)+−1(−8p)

=r+−3q+5p+4r+3q+8p

Combine Like Terms:

=r+−3q+5p+4r+3q+8p

=(5p+8p)+(−3q+3q)+(r+4r)

=13p+5r

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Evaluate 2(N + 3) if n = 5 show your work

algol [13]

ANSWER:

N = 16

STEP BY STEP EXPLANATION:

2(5+3)

2(5+3)

n=16

6 0

3 years ago

Please help pretty please.

Masteriza [31]

Answer:

reflection then translation

Step-by-step explanation:

you reflected of the y axis and then you translated 2 left and 5 up which brings you to 3

3 0

1 year ago