Suppose at any time t the number of ants in a colony is incr

Suppose at any time t the number of ants in a colony is increasing at a rate of 800 more than 1/80 of the population, measured in ants per month. Write a differential equation that describes this scenario. dP/dt = (1/80)P + 800 If there are currently 200,000 ants in the colony, how many will there be a year from now? (Round your answer to the nearest integer.) ______ ants

Solution

The differential equation becomes

dP/dt = (1/80)*P + 800

Now P = 200000

time = t = 1 year = 12 months

So, differential equation after integration w.r.t. t,

P = (1/80)*P*t + 800*t

P = (1/80)*200000*12 + 800*12 = 30000 + 9600 = 39600 ======> Ants increased in 1 year

So, total ants after 1 year = 200000 + 39600 = 239600 ants