The population of a colony of mosquitoes grows exponentially according to the function p(t) = p0ekt .
a) if there are 1,000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days?
b) how long will it take the colony to reach 10,000 mosquitoes?

The answer to your question is:

a) P(3) = 5818 mosquitoes

b) 4 days

Step-by-step explanation:

Data

P(t) = Poekt

a)

Po = 1000 mosquitoes

Pt = 1800

t = 1 day

P(3) = ?

                          1800 = 1000 e1k

                          1800 / 1000 = e 1k

                           e 1k = 1.8

                            1k = In 1.8

                             k = 0.587

     P(3) = 1000 e (0.587)(3)

     P (3) = 1000 e 1.761

     P(3) = 5818. 2 mosquitoes

b)

P(t) = 10,000

                         10000 = 1000 e 0.587t

                         10000 / 1000 = e 0.587t

                         10 = e 0.587t

                         In 10 = in e 0.587t

                         2.3 = 0.587t

                         t = 3.92 days ≈ 4 days

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

start with a line segment pq that we will copy. mark a point r that will be one endpoint of the new line segment. set the compasses' point on the point p of the line segment to be copied. adjust the compasses' width to the point q. the compasses' width is now equal to the length of the line segment pq.

step-by-step explanation: