Need help with the 3 questions below. Thank you in advance! 1. A can of soda is
ID: 1062596 • Letter: N
Question
Need help with the 3 questions below. Thank you in advance!
1. A can of soda is taken from a room temperature where the temp. is 72F and placed into a refrigerator where the temp. is 42F. Assume that the soda cools according to Newton's Law of Cooling.
a. Assume that after 5mins. the temp. of the soda is 60F. Find the temp. of the soda after t mins. (find k to four decimal places).
b. Find the amount of time for the soda to cool to 50F.
2. Suppose an experimental population of fruit flies increases according to the law of exponential growth. The initial population was 100 and there were 300 flies after the fourth day.
a. Find the function that produces the number of flies at a time t
b. Find the time required for there to be 10,000 flies.
3. Assume that a payment of $20,000 is due in five years based on 4% interest compounded continously. Find the present value of this payment.
Explanation / Answer
according to newtons law of cooling , the rate of variation of temperature (T) with respect to time dT/dt = K(72-T)
hence dT/((T-42)= Kdt
at t=0 T= 72F
ln(T-42)= Kt+C at t= 0 T=72
Ln30 = C
C= 3.40
ln( (T-42) = Kt +3.40
at t= 5min, T=60F
ln(60-42)= K*5+3.40, K=-0.10193 T/sec
hence ln (T-42)= -0.10193t+3.40
for T=50
ln(50-42)= -0.10193t+3.40,
t=12 vmin
2. Let the variation of flies with time be represented as
Y= Ce(kt)
K and C are constants
at t=0 Y=100 Y= C* exp(0), C= 100
Hecne the original equation becomes Y= 100*e(kt)
t=4 Y=300, 300 = 100*e(4k)
e(4K)= 3
taking ln
4K = ln 3
K= ln3/4 =0.275
hence Y = 100*e(0.275t)
for Y=10000
10000 = 100*e(0.275t)
t= 16.75 days
3. for the case of interest compounded continuously
S ( Future worth)= P(Present worth)* e(rn)
S= $52000
r= rate of interest =4/100, n = number of years =5
52000= Pe(0.04*5),
P= $42574
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