Question

MEDAL AND FAN!!
A biologist is comparing the growth of a population of flies per week to the number of flies a lizard will consume per week. She has devised an equation to solve for which day (x) the lizard would be able to eat the entire population. The equation is 3^x = 5x - 1. However, she has observed that the lizard cannot eat more than seven flies in one week.

Explain to the biologist how she can solve this on a graph using a system of equations. Identify any possible constraints to the situation

Answer 1

I have all of the information on how to graph it. I just need help on the constraints.
@HELP!!!! @phi

Answer 2

cannot eat more than seven flies in one week.
that would be the line y=7, and the relation y≤7

Answer 3

it can't eat more than 8 flies per week, so we can say
f(g)≤7g where f(g) is the number of flies altogether, per number of weeks ─ g .

Answer 4

thank you1

Answer 5

per week, it is not a horizontal line, phi.

Answer 6

y≤7, is not the function for the number of flies eaten per week, because that would then mean that it can eat no more than 7 in ANY number of weeks (for whatever y-values).

It should be y≤7x

Answer 7

I don;t really see that the question is asking for just x=1... I am for some reason thinking it is for all whole numbers of x. But whatever you ...

Answer 8

Here is the graph of how to solve and my reasoning.

in the graph, the y value is the number of bugs, and x is the number of days

the curve y= 3^x represents how many bugs there are after x days
It is the blue curve, and it grows exponentially (typical of population growth)

y= 5x-1 is how many bugs are eaten after x days

I interpret the constraint "the lizard cannot eat more than seven flies in one week"
to mean that a maximum of 7 flies can be eaten in any given week (i.e. over the space of 7 days). All 7 bugs can be eaten on the first day or the last day. The constraint is that the total number eaten must be less than or equal to 7 *for the first seven days*

Based on the intersection of the two curves, there are two points where the number of bugs in the population matches the number eaten.
The first solution occurs at 0.58 days, and 1.88 bugs
The second solution occurs at 2 days, and 9 bugs eaten

We exclude the 2nd solution because it requires 9 bugs to be eaten within the same week, and we are allowed to eat only bugs.

this problem is clearly artificial, because we cannot really eat 1.88 bugs (unless we count unborn eggs as a fraction of a bug?).

Answer 9

*we are allowed to eat only 7 bugs.