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Amiraneli [1.4K]
3 years ago
15

A certain compound has a half-life of four days. Write and use an exponential decay function to find the amount of compound rema

ining from a 75-ounce sample after three weeks .
Mathematics
1 answer:
dimaraw [331]3 years ago
4 0

Answer:

1.97 ounces

Step-by-step explanation:

-The exponential decay function is given by the formula:

P_t=P_oe^{-rt}\\\\

Given that the half-life is 4 days, we can substitute in the formula to solve the rate of decay for a single half-life:

P_t=P_oe^{rt}\\\\P_t=0.5P_o\\\\\therefore 0.5=e^{-4r}\\\\-4r=In(0.5)\\\\r=0.17329

#Since, 1 week has 7 days, 3 weeks is a 21-day period, thus, t=21.

#We substitute and solve for the amount remaining after 21days of decay:

P_t=P_oe^{-rt}\\\\=75e^{-21\times 0.17329}\\\\=1.97072\\\\\approx1.97 \ oz

Hence, the amount remaining after 3 weeks of decays is approximately 1.97 ounces

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A lady buys 20 trinkets at a yard sale.
Katen [24]

Answer:

Lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.

Step-by-step explanation:

A lady buys total number of trinkets = 20

Cost of each trinket is either $0.30 or $0.65.

Let the number of trinkets is x she purchased for $0.30 and y for $0.65

Then x + y = 20 --------(1)

Since she spends total amount = $8.80

Then the equation will be

0.30x + 0.65y = 8.80 ---------(2)

We replace x = (20 - y) from equation (1) to equation (2)

0.30(20 - y) + 0.65y = 8.80

6 - 0.30y + 0.65y = 8.80

0.35y + 6 = 8.80

0.35y = 8.80 - 6

0.35y = 2.80

y = \frac{2.80}{0.35}

y = 8

Now we put y = 8 in equation (1)

x + 8 = 20

x = 20 - 8

x = 12

Therefore, lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.

7 0
3 years ago
Find the slope of the line that passes through (8, 6) and (2, 7).
Amiraneli [1.4K]
Vas happenin!!

Slope form - y2-y1/x2-x1

7-6/ 2-8

1/-6

Your slope is -6x


Hope this helps

-Zayn Malik
6 0
2 years ago
Explain how to find the absolute value of a number.
kykrilka [37]
The correct answer is C. Absolute numbers should always yield a positive value. Other choices doesn’t do that. Measuring the distance on a number line ensures the positive value without changing the magnitude of the number given.
5 0
1 year ago
Can someone please help me ASAP :)
jeyben [28]
Did this a couple years ago, im kinda lost xD . sorry
4 0
3 years ago
Ben and his three friends were ordering pizza. They could spend at most $26. If a large
lutik1710 [3]

Answer:

6 toppings

Step-by-step explanation:

The t in this equation represents the amount of toppings.

22 + 0.65t = 26

-22 -22

0.65t = 4

0.65t/0.65 = 4/0.65

t = 6

They could get 6 toppings and the total would be $25.90.

6 0
3 years ago
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