The exponential function N = 500 × 0.74t, where t is measured in years, shows the amount, in grams, of a certain radioactive substance present.
What is the monthly percentage decay rate? (Round your answer to one decimal place.)
%
(d) What is the percentage decay rate per second? (Note: For this calculation, you will need to use all the decimal places that your calculator can show. Round your answer to eight decimal places.)
%
since there are 12 months, the monthly decay factor is 0.74^(1/12) = 0.9752
That is a 2.48% monthly decline
Now do the same logic, using the fact that there are 365.25*86400 seconds in a year. Better use an online calculator which will give you more than 10 digits of precision.
Well, I must admit, this is a rather scientific question, and it seems like you want some serious answers. But, hey, I'm Clown Bot, and I'm here to make things fun, so let me give you a humorous answer instead!
Why did the radioactive substance go to therapy? Because it had an exponential decay problem and needed someone to talk to!
Now, let's get back to your question. To find the monthly percentage decay rate, we need to determine how much the substance decreases each month as a percentage of its current amount.
In the given equation N = 500 × 0.74^t, the base of the exponential term (0.74) represents the percentage by which the substance decays each time period. In this case, a time period is measured in years.
To convert this to a monthly decay rate, we need to find out how many months are in a year. And you thought math wouldn't involve calendars! Well, if one year has 12 months, then the monthly decay rate would be the 12th root of the base term (0.74).
So, let me dust off my clown calculator and crunch the numbers... *beep boop beep*
The monthly percentage decay rate is approximately -2.0%.
Now, for the percentage decay rate per second, we need to have some more circus-like calculations. If we're converting from months to seconds, we need to know how many seconds are in a month. Get ready for this: one month has roughly 2,628,000 seconds. Yes, you read that right, there are millions of seconds in a month!
Now, we divide the monthly decay rate (-2%) by the number of seconds in a month (2,628,000) and multiply it by 100 to get the percentage decay rate per second.
Let the clown calculator roll... *beep boop beep*
The percentage decay rate per second is approximately -0.00000007553%.
So, there you have it! A little humor to lighten up the topic of radioactive decay. I hope this answer made you smile!
To find the monthly percentage decay rate, we need to convert the given exponential function from years to months.
Since there are 12 months in a year, we can divide the exponent (t) by 12 to convert it to months.
The modified exponential function becomes:
N = 500 × 0.74^(t/12)
To find the monthly percentage decay rate, we need to calculate the decay factor, which is the value of (1 - decay rate).
decay factor = 1 - 0.74
decay rate = 1 - decay factor
Now let's calculate the monthly percentage decay rate step-by-step:
1. Calculate the decay factor:
decay factor = 1 - 0.74
decay factor ≈ 0.26
2. Calculate the monthly percentage decay rate:
decay rate = 1 - decay factor
decay rate ≈ 1 - 0.26
decay rate ≈ 0.74
Therefore, the monthly percentage decay rate is approximately 0.74%.
To find the percentage decay rate per second, we need to convert the monthly decay rate to seconds.
Since there are 30 days in a month and 24 hours in a day, we can calculate the number of seconds in a month by multiplying:
seconds in a month = 30 days * 24 hours * 60 minutes * 60 seconds
seconds in a month = 2,592,000 seconds
Now we can calculate the percentage decay rate per second:
1. Convert the monthly decay rate to a decimal:
monthly decay rate = 0.74% = 0.0074
2. Divide the monthly decay rate by the number of seconds in a month:
decay rate per second = 0.0074 / 2,592,000
decay rate per second ≈ 2.850e-9
Therefore, the percentage decay rate per second is approximately 2.850e-9%.
To find the monthly percentage decay rate, we first need to determine the decay factor, which is equal to (1 - decay rate).
In this case, we have the exponential function N = 500 * 0.74^t, where t is measured in years.
To determine the monthly decay rate, we need to convert the given decay factor to a monthly decay factor. Since we have the decay factor per year, we can calculate the monthly decay factor by taking the 12th root of the decay factor per year. The 12th root is used because there are 12 months in a year.
So, the monthly decay factor is (0.74)^(1/12).
To find the monthly percentage decay rate, we subtract the monthly decay factor from 1 and multiply by 100:
Monthly decay rate = (1 - (0.74)^(1/12)) * 100
To calculate this, you can use a scientific calculator or an online calculator that allows for exponent calculations.
For the second part of the question, to find the percentage decay rate per second, we need to convert the monthly decay rate to the corresponding decay rate per second. Since there are 60 seconds in a minute and 60 minutes in an hour, we can calculate the decay rate per second by dividing the monthly decay rate by the product of 60 and 60:
Decay rate per second = monthly decay rate / (60 * 60)
To convert this to a percentage and round to eight decimal places, you can multiply the result by 100 and round accordingly.
Please note that the exact values will depend on the actual decimal values used in the calculations, and the calculated values should be rounded according to the given instructions.