Question

Sodium-24 has a half-life of 15 hours. How many grams of a 900 g sample will remain after 90 hours?

28.125 g

14.0625 g

7.5 g

7.03125 g

Answer 1

how many half-lives of Na-24 is 90 hours?

Answer 2

15

Answer 3

one half life is 15 hours, how many half lives is 90 hrs?

Answer 4

im really struggling with this sorry

Answer 5

1350

Answer 6

every half life, the mass is reduced by half

Answer 7

the number of half lives is 90hr / 15 hr = ?

Answer 8

so its 6

Answer 9

yes, 6 half lives,

so divide the original mass in half, 6 times.


ie 900/2^6

Answer 10

14.0625

Answer 11

yep, [unit is grams]

Answer 12

so is this my answer

Answer 13

does it make sense yet?


initially the sample is 900g

after 15hr : 450g

...30hr : 225g
.
.
.
90hr : 14 g

Answer 14

yes

Answer 15

but can you help me with one more problem as well

Answer 16

ok

Answer 17

A research study in 2000 found that there were 440 coyotes in a given region. The coyote population is expected to grow at a rate of 17% each year. In what year will the population first exceed 10,000?

Answer 18

year coyotes
2000 440
2001 440*114%
2002 440*114%*114%

200n 440*(114%)^n

Answer 19

where did you get the 114

Answer 20

ops 100% + 17% = 117%
(not 114%)

Answer 21

ok so it would be 440(1+.17)^

Answer 22

yeah something like that/this
\[N(t) = 440\times(117\%)^t\]

Answer 23

What value of t makes N = 1000

Answer 24

ie, set N(t) = 1000, and solve for t

Answer 25

wait can you explain the 1000 part

Answer 26

[damnit, i cant read very well today]

The question say `In what year will the population first exceed 10,000?`

so set N(t) = 10,000

Answer 27

so do i multiply to 10,000 by a number

Answer 28

\[10,000=440(117\%)^t\]divide both sides by 440,

then . . .

Answer 29

this is the part i didnt understand

Answer 30

do i divide 10,000 by 440 and by 1.17

Answer 31

\[10,000=440(117\%)^t\\
\frac{10,000}{440}=(117\%)^t\]

Answer 32

now you have an exponential, to simplify this , use logs

Answer 33

i got 22

Answer 34

so does t=22

Answer 35

so it would take 22 years

Answer 36

\[10,000=440(117\%)^t\\
\frac{10,000}{440}=(117\%)^t\\
22.7 = (117\%)^t\\
22.7 = 1.17^{t}\\
\log_{1.17}22.7 = \log_{1.17}1.17^{t}\\[2ex]
\log_{1.17}22.7=t\]

Answer 37

now use the change of base formula

\[\log_ba=\frac{\ln a}{\ln b}\]

Answer 38

so the year would be 2022

Answer 39

how did you get 22?

Answer 40

i dont know

Answer 41

[well its not correct]

Answer 42

what do you get when you simplify \[\log_{1.17}22.7\]?

Answer 43

(use a calculator)