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:
Positive Correlation
EXPLANATION:
Use linear combination to solve this. It is much faster than substitution. I would start by multiplying the bottom equation by -1.
<span>4x-7y=3
-x+7y=15</span>
Then, add the two equations together. The result is:
3x=18.
You've eliminated one variable. Now you can solve for the other one.
Divide both sides by 3 to get
x=6
Plug this into one of the original equations, then solve for y
-(6)+7y=15
7y=21
y=3
Check your work by plugging these values into both equations to see if they remain true
Answer: No Solution
Step-by-step explanation:
y=2x+1 and 2x-y=3
Substitute y=2x+1 into 2x-y=3
So you will have: 2x-2x+1=3
Then,
2x-2x=0
0+1=3
1=3
1 doesn't equal 3 so there is no solution.
Answer:
x=130;
Step-by-step explanation:
70+(x-20)=180
-70 -70
x-20=110
+20 +20
x=130
