Question

The bacteria increases at the rate proportional to the number of bacteria present. If the original number 'N' doubles in 4 h, then the number of bacteria in 12 h will be ____________.

Options

• 4 N

• 8 N

• 6 N

• 3 N

Answer 1

The bacteria increases at the rate proportional to the number of bacteria present. If the original number 'N' doubles in 4 h, then the number of bacteria in 12 h will be 8 N.

Explanation:

Let P be number of bacteria present any time t

∴ `"dP"/"dt"` = kP

`"dP"/"P"` = kdt = `int "dP"/"P"` = kdt

log P = kt + C

When t = 0, then P = N

∵ C = log N

∴ log P = kt + log N

log `"P"/"N"` = k(t)

When t = 4, then P = 2N

∵ log `(2"N")/"N"` = 4k

k = `1/4 log 2`

∵ log `"P"/"N" = 1/4 log 2 ("t")`

Put, t = 12

∵ log `"P"/"N" = 12/4 log 2` = 3 log 2 = log 8

∴ `"P"/"N"` = 8

P = 8 N