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
click here to see the step by step calclation
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
click here to see the step by step calculation
after 36 days the population will reach 1000000.