Answer:
The biologist can graph two functions, one for the flies population growth and one for the flies the iguana can eat, and see that they intersect at two points (0, 0) and (1, 3).
The constraints are:
0 < x ≤ 7
1 ≤ y ≤ 8
Therefore, the only solution to the equation can be (1, 3).
Step-by-step explanation:
In order to solve the equation 3ˣ = 2x + 1, the biologist can break it into two parts.
The function for the popuation growth is: f(x) = 3ˣ
The function for the number of flies eaten is: g(x) = 2x + 1
Then, he can graph both functions (I used Geogebra, the graph is attached) and see where they intersect, which means the points where f(x) = g(x). Algebrically, it means find the soutions to the system:
From the graph we can see that the two functions intersect at (0, 0) and (1, 3). In order to see if these solutions are acceptable, we need to set the constraints.
We know that x represents the number of days in a week, therefore: 0 < x ≤ 7 (we cannot have 0 days, and they cannot be more than or equal to 7).
We also know that y represents the number of flies, therefore: 1 ≤ y ≤ 8 (we need to start with at least a population of 1 fly and we cannot have more than 8 flies eaten per week).
Due to these restraints, we have to reject the solution (0, 0) which would have no sense.
Hence, by graphing the two functions and setting the restraints, the biologist can find that (1, 3) solves his equation. This means that after 1 day the iguana would eat the entire population of 3 flies.