Hi there!
im not sure how to do this word problem. Which numbers do I put where to solve?
thanks :)
Explanation (1)
Student Explanation
January 15, 2024
Hi!
First of all, it is important to understand that you have an exponential function. Therefore, we will be working with this equation :
where f(x) is the number of ants and x the number of days since the start of the study.
We know that the population doubles in size every 4 days. This information gives us our parameters b and c, which are respectively 1/4 and 2. Indeed, our multiplier is 2 since the population doubles
$$ c=2$$
and the event occurs every 4 days, but the variable x is in days. There is 1 event every 4 days.
$$ b = \frac{1}{4}$$
Which gives us so far this equation :
$$ f(x) =a(2)^{\frac{1}{4}x}$$
$$ f(x) =a(2)^{0,25x}$$
We want to find how many ants were in the colony at the start of the study, therefore the value of our parameter \(a\), the initial value. We know that after 5 days, there are 6400 ants, which gives us the point (5, 6400). To find the value of \(a\), we can insert the coordinates of this point into our equation, like this :
$$ 6400 =a(2)^{\frac{1}{4} \times 5}$$
We will then be able to find the value of \(a\), our initial number of ants.
Here's a page that shows similar examples : Problem Solving with the Exponential Function | Secondaire | Alloprof
I hope I was able to help you! Feel free to ask us more questions if you have any! :)
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