Question

a population of insects increases at a rate of 1.5% per day about how long will it take to double A)2.5 days b) 5.0 days c) 46.6 days or d) 66.7 days

Answer 1

D) 66.7 days
Because .015 (1.5%) multiplied by 66.7 is equal to 1.0005 or approximately 100% which would be double the population.

Answer 2

We can use population formula

$P(t)=P_0(1+r)^{t}$

we are given

interest rate is 1.5% per day

so,

$r=0.015$

now, we can plug values

$P(t)=P_0(1+0.015)^{t}$

$P(t)=P_0(1.015)^{t}$

we are given

P(t)=2Po

we can plug it

$2P_0=P_0(1.015)^{t}$

we can solve for t

$2=(1.015)^{t}$

$t=46.55$

so,

number of days is 46.5..........Answer