Application of calculus (1 Viewer)

[atakach99]

heyy i have two questions that i am having trouble solving

1)A population in a certain city is growing at a rate proportional to the population itself. After 3 years the population increases by 20%. How long will it take for the population to double?

2) The half-life of radium is 1600 years.
a) Find the percentage of radium that will be decayed after 500 years.
b)Find the number of years that it will take for 75% of the radium to decay.

 

[conics2008]

i) assume when t=0 P=1000 and go on to find A andk and then find t by subbin in 2000 into the equation and find t .. you need to make up your own condition.

 

[cwag]

1) let P= population and P_o = original population, k is a constant, and t is time in years

P= P_oe^kt
when t=3 P=1.2P_o

so, 1.2P_o=P_oe^3k
1.2 = e^3k
(ln 1.2)/3 = k
k = 0.06077...

Now, for double population
P = 2P_o
2P_o=P_oe^0.06077t
(ln 2)/0.06077 = t
t= 11.4 years

question two is similar...try and do it now