A culture started with 2,000 bacteria. After 2 hours, it grew to 2,400 bacteria. Predict how many bacteria will be present after 10 hours?

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Answer 1 · 2016-08-29T16:13:09

4977 bacteria.

Growth with bacteria is exponential, so we can consider that we are working with a G.P.

#a = 2000#

#r = 2400/2000 = 1.2#

If we regard 2 hours as being one time unit, 10 hours is a further 4 units of time. (6th term)

Either 4 more starting with 2400 bacteria,
or 5 time units starting with 2000 bacteria.

After 10 hours: 2000 xx 1.2^5 = 4977 bacteria.

#T_6 = 2000 xx 1.2^5#

Or

#T_5 = 2400 xx 1.2^4#