Question
The population of a certain community is increasing at a rate directly proportional to the population at any time t. In the last yr, the population has doubled.
How long will it take for the population to triple?
Round the answer to the nearest hundredth, if necessary.
How long will it take for the population to triple?
Round the answer to the nearest hundredth, if necessary.
Answers
this fits the standard
A = a e^(kt), where a is the initial amount, A is the new amount, k is a constant and t is the time in suitable units.
in our case if a=1 , A = 2, t = 1
2 = 1 e^k
ln 2 = ln e^k
k = ln2
A = e^ (ln2 t)
when A = 3
3 = e^ ln2 t
ln2 t = ln3
t = ln3/ln2 = 1.58 days
or , since we have a case of "doubling"
N = 1 (2)^t
3 = 2^t
ln3 = ln 2^t
ln3 = t ln2
t = ln3/ln2 , as above
A = a e^(kt), where a is the initial amount, A is the new amount, k is a constant and t is the time in suitable units.
in our case if a=1 , A = 2, t = 1
2 = 1 e^k
ln 2 = ln e^k
k = ln2
A = e^ (ln2 t)
when A = 3
3 = e^ ln2 t
ln2 t = ln3
t = ln3/ln2 = 1.58 days
or , since we have a case of "doubling"
N = 1 (2)^t
3 = 2^t
ln3 = ln 2^t
ln3 = t ln2
t = ln3/ln2 , as above
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