A function m(t)= m₀e^(-rt) that models the mass remaining after t years is; m(t) = 27e^(-0.00043t)
The amount of sample that will remain after 4000 years is; 4.8357 mg
The number of years that it will take for only 17 mg of the sample to remain is; 1076 years
<h3>How to solve exponential decay function?</h3>
A) Using the model for radioactive decay;
m(t)= m₀e^(-rt)
where;
m₀ is initial mass
r is rate of growth
t is time
Thus, we are given;
m₀ = 27 mg
r = (In 2)/1600 = -0.00043 which shows a decrease by 0.00043
and so we have;
m(t) = 27e^(-0.00043t)
c) The amount that will remain after 4000 years is;
m(4000) = 27e^(-0.00043 * 4000)
m(4000) = 27 * 0.1791
m(4000) = 4.8357 mg
d) For 17 mg to remain;
17 = 27e^(-0.00043 * t)
17/27 = e^(-0.00043 * t)
In(17/27) = -0.00043 * t
-0.4626/-0.00043 = t
t = 1076 years
Read more about Exponential decay function at; brainly.com/question/27822382
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Let's multiply each of the four squares, one by one.
In blue, we see the dimensions are x by x. x times x = x^2
In pink, we see the dimensions are 9 by x. x times 9 = 9x
In green, the dimensions are x by 3. 3 times x = 3x
And finally, yellow's dimensions are 3 by 9. 3 times 9 = 27
We can now just add all these areas to find the total area:
x^2 + 12x + 27
3:1 is a common example, or even like 4:3
Answer:
Thus the number of books at $2 is 9 books.
Step-by-step explanation:
The number of the book purchased = 15 books
Total amount spend to buy the books = $34
The prices of books are $2 and $3.
Let the number of books purchased at price $2 = x
Let the number of books purchased at price $3 = y
Now we have to find the number of books that is bought at $2.
Below are the equations.
x + y = 15
2x + 3y = 34
Now solve for the x,
x + y = 15
y = 15 – x
Now insert it in the 2x + 3y = 34
2x + 3(15-x) = 34
2x + 45 – 3x = 34
-x = 34 – 45
x = 9
Thus the number of books at $2 is 9 books.