The function must have the form
N(t) = a e^kt , where a is the intitial number and k is a constant , and t is in minutes
for t=0 , a = 10000
for t = t1
20000 = 10000 e^(kt1)
2 = e^(kt1)
for t = t1+10
100000 = 10000 e^(k(t1+10)
10 = e^(kt1 + 10k)
divide the two equations
5 = e^(10k)
ln5 = 10klne
10k = ln5
k = ln5/10
a) N(t) = 10000 e^(ln5/10 t)
when t = 20
N(20) = 10000 e^(ln5/10 (20)) = 250 000
c) when N(t) = 20000
2 = e^(ln5/10 t)
ln2 = ln5/10 t
t = 10ln2/ln5 = 4.3067
so in effect we found the "doubling time" to be appr. 4.307 minutes
(we can now also check if for t = 4.307 + 10 or t=14.307 we get N = 50000
10000 e^(ln5/10 (14.307))
= 10000 e^2.302623
= 100 004 , not bad
Calculus - for f(x)=-x^2 +1, which value is the largest magnitude? a) average ...
calculus - The length l of a rectangle is decrasing at a rate of 5 cm/sec while ...
Calculus Please Help - Given the numerical values shown for the function f(x), ...
calculus - Let F(s)=5s2+1s+4. Find a value of d greater than 0 such that the ...
Calculus - Let F(s)=5s2+5s+4 . Find a value of d greater than 0 such that the ...
calculus (rate of change) - consider the function f(x)=x^2-6x+12 a. find the ...
calculus - Let f be defined as follows. F(x)=y=x^2 -7 (a) Find the average rate ...
Math - Could someone help me with these questions, I don't know question c) and ...
Math~Reinyyy - Could someone help me with these questions, I don't know ...
Calculus - y = f(x) = x^2 - 6 x (a) Find the average rate of change of y with ...