# A type of bacteria has an exponential grow rate at 70% every hour, what is the number of bacteria after 10 hr, 1 day and 3 days. The bacteria have an exponential growth rate of 70%. The formula for the exponential growth rate can be given by x (t) = a*b^ (t/T), where a is the initial number of bacteria, b is the increase in time T.

Here we have the initial number as 5. The population...

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The bacteria have an exponential growth rate of 70%. The formula for the exponential growth rate can be given by x (t) = a*b^ (t/T), where a is the initial number of bacteria, b is the increase in time T.

Here we have the initial number as 5. The population of bacteria increases by 0.7 in an hour.

Therefore in

10 hours, the number of bacteria is 5*(1.7)^(10/1)

=> 5*(1.7)^10

=> 1007 bacteria.

In 1 day:

=> 5* (1.7) ^24

=> 1697243

In 3 days:

=> 5*(1.7)^72

=> 1.955* 10^17

Therefore the number of bacteria in 1 hr, 1 day and 3 days are:

1007, 1697243 and 1.955* 10^17 resp.

Approved by eNotes Editorial Team