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1.11.8 Interpreting solutions of differential equations (A-level only)

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Question 3

The hourly rate of increase of a bacteria colony is equal to 5% of the current size of the colony. N N\,N is the number of bacteria in thousands and t t\,t is the time in hours.

a.

Write down a differential equation for this relationship.

[2]
b.

Show that N=Ae0.05tN = Ae^{0.05t}N=Ae0.05t where A A\,A is a constant.

[4]
c.

Given that the initial number of bacteria is 4000. Find the number of bacteria after 8 hours to 3 significant figures.

[2]

1.11.8 Interpreting solutions of differential equations (A-level only) Questions

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  3. /1.11.8 Interpreting solutions of differential equations (A-level only)