Problema Solution

A population of critters exhibits natural exponential growth. intial population is 500. after 3 days it is 950. what will be the population after 10 ddays? when will the population reach 1000000

Answer provided by our tutors

the population is modeled by the equation


y = y0 * (e^(rt))


where


y0 = 500 is the initial population

t = the number of days

r = rate of growth we need to find


the exponential equation to represent the cell population is


y = 500 * (e^(rt))


for t= 3 days, y = 950


500 * (e^(3r)) = 950


r = (1/3)ln(950/500)


r = 0.214


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for t = 10 we have


y = 500 * (e^(10*0.214))


y = 4250 critters


After 10 days there will be 4250 critters.


we need to find t for y = 1000000


1000000 = 500 * (e^(0.214t))


t = (1/0.214)ln(1000000/500)


t = 36 days


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after 36 days the population will reach 1000000.