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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Answer:
a)120
b)6.67%
Step-by-step explanation:
Given:
No. of digits given= 6
Digits given= 1,2,3,5,8,9
Number to be formed should be 3-digits, as we have to choose 3 digits from given 6-digits so the no. of combinations will be
6P3= 6!/3!
= 6*5*4*3*2*1/3*2*1
=6*5*4
=120
Now finding the probability that both the first digit and the last digit of the three-digit number are even numbers:
As the first and last digits can only be even
then the form of number can be
a)2n8 or
b)8n2
where n can be 1,3,5 or 9
4*2=8
so there can be 8 three-digit numbers with both the first digit and the last digit even numbers
And probability = 8/120
= 0.0667
=6.67%
The probability that both the first digit and the last digit of the three-digit number are even numbers is 6.67% !
Answer: y= -2x + 24
Step-by-step explanation
2x - 4y = 24
subtract 2x from both sides
divide 4y by 4y to get y by itself
then you get y= -2x + 24
25/52 25 is the numerator
52 is the denominator
