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1 answer:
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Answer:
a) , b)
, c)
, d)
Step-by-step explanation:
a) Let assume an initial mass m decaying at a constant rate k throughout time, the differential equation is:
b) The general solution is found after separating variables and integrating each sides:
Where is the time constant and
c) The time constant is:
The particular solution of the differential equation is:
d) The amount of radium after 300 years is:
Answer:
a) the trigonometric function is;
b) ( to two decimal places)
Step-by-step explanation:
This data can be represented by the sinusoidal function of the form :
where A = amplitude and which can be determined via the formula:
A = 7.5° C
where B = the frequency;
Since the data covers a period of 3 days ; then
( where 365 is the time period )
The vertical shift is found by the equation D;
D =
D =
D = 21.5
Replacing the values of A ; B and D into the above sinusoidal function; we have :
From the question; when it is 7th of the year ( i.e January 7);
t = 7 and the temperature (y) = 29° C
replacing that too into the above equation; we have:
Thus; the trigonometric function is;
Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :
( to two decimal places)