A population of 170 crickets doubles in size every month. How many crickets
will there be after 2 years?

Question

A population of 170 crickets doubles in size every month.  How many crickets
will there be after 2 years?

shaleiah · Answer

@Michele_Laino

mathmale · Answer

Lot of crickets!  Their count will have doubled 24 times (as there are 24 months in 2 years).  What would be an appropriate formula for calculating the population of crickets after 24 months?

mathmale · Answer

To answer this, create an EXPONENTIAL

shaleiah · Answer

Alright. Mind giving me a moment?

mathmale · Answer

EQUATION and let n represent the number of times the population doubles.

Have you done this kind of problem before?  If so, type out the exponential growth model.

shaleiah · Answer

170*24^2=n

shaleiah · Answer

@Directrix

mathmale · Answer

The general formula for expo growth that I was looking for is$$y=a*e ^{kt}$$

mathmale · Answer

and we have to find the values of a and k from the given info.

At the very beginning, t=0 and the population is 170.   What is the value of the coefficient a?

directrix · Answer

Do you know the doubling formula?  @shaleiah

directrix · Answer

You have it slightly off in your post: 170*24^2=n

n = 170 ( (2) ^ 24 )

shaleiah · Answer

2,852,126,720

shaleiah · Answer

:D

michele_laino · Answer

hint:
at first month the population is 170
at second month the population is 2*170
at the third month the population is $2 \cdot 2 \cdot 170= 2^{(3-1)} \cdot 170$
at fourth month the population is $2^{(4-1)}\cdot 170$ 
...
at the 24th month the population is $2^{(24-1)}\cdot 170$

directrix · Answer

I think the person starts with 170 crickets and has 340 at the end of month 1.

mathmale · Answer

I agree.  However, it might be easier to find the value of the growth constant, k, in $$y=a*e ^{kt}$$

mathmale · Answer

If t=0, then y=a(1).  But the initial value of y (initial population) is 170; therefore, a = 170.

All you hae to do now is the find the value k of the growth constant.

michele_laino · Answer

please what are the corresponding options

shaleiah · Answer

Sorry, no options.

directrix · Answer

These may be they:
a.	2,852,126,720 crickets	c.	8,160 crickets	   
b.	680 crickets	d.	680 crickets

michele_laino · Answer

In my reasoning, I started to count from $1$

michele_laino · Answer

please I ask this:
after 2 month what is the population?

michele_laino · Answer

months*

michele_laino · Answer

I think it is 170 at the first month and 170*2=340 at the second month

michele_laino · Answer

I think that the common sense suggests that reasoning