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3 years ago

The half-life of a radioactive substance is 12 days. After 11 days a sample of the substance has been reduced to a mass of 7 mg.

Mathematics

2 answers:

Sloan [31]3 years ago

8 0

There is 8mg in all and that’s the answer

8_murik_8 [283]3 years ago

3 0

Answer:

13.21 grams
84.6 days

Step-by-step explanation:

The mass (m) remaining will be a function of the initial mass (m0) and the time in days (t) according to the exponential decay formula ...

m = m0(1/2)^(t/12)

a) You want to find m0 for m=7 and t=11. Put these numbers in the formula and solve for m0.

7 = m0(1/2)^(11/12) = 0.529732×m0

m0 = 7/0.529732 = 13.21 . . . . grams

The initial mass of the sample was 13.21 grams.

b) We can use the value of m0 we found to determine the number of days until 0.1 mg will remain:

0.1 = 13.21(1/2)^(t/12)

Dividing by 13.21 and taking logs, we have ...

log(0.1/13.21) = (t/12)log(1/2)

t = 12·log(0.1/13.21)/log(1/2) = 84.55

There will be only 0.1 mg left after 84.6 days.

_____

<em>Comment on the calculations</em>

For the latter part of the problem, be sure to use the full-precision value of m0. Do not round any results until the final answer. Alternatively, you could use 7 mg for m0 and add 11 days to the result you get.

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3 years ago

Help plzzz thank you !

VashaNatasha [74]

Answer:

a. Ameribank-$15,157.50

b. Capital Two-$4,646.25

Step-by-step explanation:

a. Tad's savings is $15,000, we calculate his total amount at the end of the year for each bank:

#Ameribank

$A=P+I=P+PRT\\\\=15000+15000\times 0.0105\times 1\\\\=\$15,157.50$

#Huffington( we use the effective rate to calculate the compound amount):

$i_m=(1+i/m)^m-1\\\\=(1+0.0095/12)^[12}-1=0.009541\\\\A=P(1+i_m)^n\\\\=15000(1.009541)^1\\\\=\$15,143.12$

#Sixth-Third, Take 1 yrs=52 weeks:

$i_m=(1+i/m)^m-1\\\\=(1+0.01/52)^{52}-1=0.01005\\\\A=15000(1.01005)^1\\\\=\$15,150.74$

#Hence, Ameribank is the best option as his money grows to $15,157.50 which is greater than all the remaining two options.

b. We use the compound interest formula $A=P(1+r/n)^{nt}$ to determine which bank gives the best option:

#Capital Two. r=3.75%, n=12,t=4

$A=P(1+r/n)^{nt}\\\\=4000(1+0.0375/12)^{12\times4}\\\\=\$4,646.25$

#J.C Morgan, t=2, r=3.55% n=12

$A=P(1+r/n)^{nt}\\\\=4000(1+0.0355/12)^{12\times 2}\\\\=\$4,293.87$

#Silverman Slacks, n=12,t=3, r=3.65%

$A=P(1+r/n)^{nt}\\\\=4000(1+0.0365/12)^{12\times3}\\\\=\$4,462.14$

We compare the investment amounts after t years:

$Capital>Silver>Morgan=4646.25>4462.14>4293.87$

Hence, Capital two is the best option with an investment amount of $4,646.25

8 0

3 years ago

Read 2 more answers

You are working a part-time job working 20 hours a week. After a week you earn $312. How much do you earn hourly? Write an equat

Lubov Fominskaja [6]

Firstly figure out how much money you earn per one hour. This is 312$ divided by 20 is 16$/hour. Then write an equation which represents only hourly earnings: y = 16x. To answer the last question just enter the value for variable x = 15, and you will get money earned per one week.

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3 years ago