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3 years ago

9

a radioactive substance has a half-life of 2 seconds. A scientist begins with a sample of 20 grams. How much of the substance re

mains after 8 seconds?

1 answer:

s344n2d4d5 [400]3 years ago

5 0

Answer:

1.25 g

Step-by-step explanation:

you start with 20g at 0 seconds.

divide by half after 2 seconds and you have 10g.

at 4 seconds you have 5g.

at 6 seconds you have 2.5g.

at 8 seconds you have 1.25g.

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Roger works part-time as a waiter at a pizza joint. He earns $9 per hour. How much does he earn for 20 hours of work?

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Answer:

180

Step-by-step explanation:

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How long will it take for $2500 to double if it is invested at 6% annual interest compounded 6 times a year? Enter exact calcula

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Answer:

Part 1) $t=11.610\ years$

Part 2) $t=11.552\ years$

Step-by-step explanation:

Part 1) we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06\\n=6$

substitute in the formula above

$5,000=2,500(1+\frac{0.06}{6})^{6t}$

$2=(1.01)^{6t}$

Apply log both sides

$log(2)=log[(1.01)^{6t}]$

$log(2)=(6t)log(1.01)$

solve for t

$t=log(2)/[6log(1.01)]$

$t=11.610\ years$

Part 2) we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06$

substitute in the formula above

$5,000=2,500(e)^{0.06t}$

$2=(e)^{0.06t}$

Apply ln both sides

$ln(2)=ln[(e)^{0.06t}]$

$ln(2)=(0.06t)ln(e)$

$ln(2)=(0.06t)$

$t=ln(2)/(0.06)$

$t=11.552\ years$

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3 years ago

NEED HELP ASAP!!!

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Answer D

Step-by-step explanation:

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Estimate the area of the rectangle at the right. 6 1/4 ft and 10 5/6

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Answer:

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