2 points) Two populations are studied. Population 1 is found to obey the differe

Question

2 points) Two populations are studied. Population 1 is found to obey the differential equation dy, ldt = ly, and population 2 obeys dy2ldt =-0.5y2 where is time in years. (a) Which population is growing and which is declining? A. Both are declining B. yi is growing and yz is decreasing C. Not enough information to tell. D. Both are growing E. yi is decreasing and y2 is growing Enter the letter corresponding to the correct answer ? (b) Find the doubling time (respectively half-life) associated with the given population. Give your answers to at least three significant figures. Doubling time Half-Life= years years (cir the initial levels of the two populations were y' (0) = 90 and y2 (0) = 14000, how big would each population be at time t ? G) M2(r) = d) At what time would the two populations be exactly equal? Give your answer to at least three significant figures Time years

Explanation / Answer

a)

Integrating gives

y_1=A exp(t)

y_2=B exp(-0.5t)

A. y_1 is growing and y_2 is declining

b)

2A=A exp(t)

t=ln(2)

Doubling time =ln(2)

A/2=A exp(-0.5 t)

ln(2)=t/2

t=2 ln(2)

Half life =2 ln(2)

c)

y_1= 90 exp(t)

y_2= 14000 exp(-0.5t)

d)

y_1=y_2

90 exp(t)=14000 exp(-0.5t)

exp(1.5t)=1400/9\

tpprox 3.365

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