1. 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. 2. A quantity grows exponentially at the rate of 7.00% per year for 7 years. Find the final amount if the initial amount is 201 units. Round your answer to the nearest integer. please kindly help me with this questions... ill give an brilliant ans mark this is not fun.. honestly i need an solution to this questions.. answer it as soon as possible
Answers
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
______________________
Let say units = x
Then dx /dt = 0.07x ( t is in years)
=> dx/ 0.07x = dt
integrating both side
(1/0.07) ln (x) = t + c₁
=> ln (x) = 0.07t + c
at t = 0 , x = 201
ln (201) = + c
=> c = 5.303
after 7 years
=> ln(x) = 0.07(7) + 5.303
=> ln(x) = 5.793
=> x = 328
328 is the final amount if the initial amount is 201 units
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