The strain of bacteria will double in size and then divide every 20 min. Let a, be the initial number of bacteria cells, a, the number after 20 min, and a, the number after 20(n-1) min. (a) Write a formula for the nth terma, of the geometric sequence a,, a2, ag, .., an, ... (b) Determine the first value forn where a,>1,000,000 ifa, =500. (c) How long does it take for the number of bacteria to exceed one million?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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The strain of bacteria will double in size and then divide every 20 min. Let a, be the initial number of bactería cells, a, the number after 20 min and a, the number
after 20(n-1) min.
(a) Write a formula for the nth terma, of the geometric sequence a1, a2, a3, .., an, ...
(b) Determine the first value for n where a,>1,000,000 if a, =500.
(c) How long does it take for the number of bacteria to exceed one million?
Transcribed Image Text:The strain of bacteria will double in size and then divide every 20 min. Let a, be the initial number of bactería cells, a, the number after 20 min and a, the number after 20(n-1) min. (a) Write a formula for the nth terma, of the geometric sequence a1, a2, a3, .., an, ... (b) Determine the first value for n where a,>1,000,000 if a, =500. (c) How long does it take for the number of bacteria to exceed one million?
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