Agroup of scientists are studying a new species of insects. they observe the patterns of 6 insects. the scientists find that the insect population, x, is growing exponentiall 20% per month. which equation can be used to find how many months, t, will it take for there to be a population of 477 insects?

(B)

Step-by-step explanation:

we can use formula

where

Po is the initial population

r is the growth rate

t is the time in months

We are given

initial population of insects

so, Po=6

The scientists find that the insect population, x, is growing exponentially 20% per month

so, r=0.20

now, we can plug these values

there to be a population of 477 insects

so, P(t)=477

now, we plug it

and we get

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1