A pharmaceutical company makes a vaccine-producing bacterium that grows at a rate of 1.7% per hour. How many units of this organism must the company have initially to have 1000 units after 5 days? Round to the nearest unit.
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Answer:
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Given : A pharmaceutical company makes a vaccine-producing bacterium that grows at a rate of 1.7% per hour.
To find : How many units of this organism must the company have initially to have 1000 units after 5 day
Solution:
Let say units = x
Then dx /dt = 0.017x ( t is in hrs)
=> dx/ 0.017x = dt
integrating both side
(1/0.017) ln (x) = t + c₁
=> ln (x) = 0.017t + c
1000 units after 5 days
5 days = 5 * 24 = 120 hrs
=> ln(1000) = 0.017(120) + c
=> 6.908 = 2.04 + c
=> c = 4.868
at t = 0
ln (x) = c
=> ln (x) = 4.868
=> x = 130
130 units of this organism must the company have initially to have 1000 units after 5 days
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