The local zoo keeps track of how many dragonflies are breeding in their insect exhibit each day.
Day: 1, 2, 3, 4, 5
Dragonflies: 9, 18, 36, 72, 144
It's exponential growth.
A. Write an equation for the function that models the data.
B. Use your equation to determine the # of dragonflies that will be breeding after 9 days
look at this chart
1 9 = 9(2^0)
2 18 = 9(2^1)
3 36 = 9(2^2)
did you notice the pattern
dragonflies = 9(2^(day - 1) )
so when day = 9
we have 9(2^8) = 2304
A. Well, it looks like those dragonflies are getting quite busy multiplying! To find an equation that models the data, we can observe that the number of dragonflies is doubling each day. So, we can start with the initial number of dragonflies, which is 9, and then multiply it by 2 raised to the power of the day number.
The equation would be:
Dragonflies = 9 * 2^(Day-1)
B. To find the number of dragonflies after 9 days, we simply substitute Day = 9 into the equation:
Dragonflies = 9 * 2^(9-1)
Dragonflies = 9 * 2^8
Dragonflies = 9 * 256
Dragonflies = 2,304
So after 9 days, there will be 2,304 dragonflies buzzing around. You better watch out, that's a lot of wings flapping!
A. To find an equation that models the data, we can observe that the number of dragonflies seems to be doubling each day. We can express this exponential growth using the formula for compound interest:
P = P0 * (1 + r)^t
In this case, P0 represents the initial number of dragonflies, r represents the growth rate (which is 1 since it is doubling each day), t represents the number of days, and P represents the final number of dragonflies.
The initial number of dragonflies (P0) is given as 9 on day 1 (t=1). Substituting these values into the formula, we get:
P = 9 * (1 + 1)^t
B. To determine the number of dragonflies that will be breeding after 9 days, we can substitute t=9 into the equation we found in part A:
P = 9 * (1 + 1)^9
Simplifying this equation will give us the answer.
To find the equation that models the data, we can observe that the number of dragonflies is doubling each day. This indicates exponential growth.
Let's assume that the initial number of dragonflies on day 1 is given by "a," and the growth factor is given by "r."
Therefore, the equation for the exponential growth can be written as:
Dragonflies = a * (r^day)
Using the given data, we can plug in the values to find the growth factor (r).
On day 1: Dragonflies = a * (r^1) = 9
On day 2: Dragonflies = a * (r^2) = 18
Dividing the second equation by the first equation: (a * (r^2)) / (a * (r^1)) = 18/9
Simplifying: r^2 / r^1 = 2
Therefore, r^1 = 2
Taking the square root of both sides: r = √2
Now that we have the growth factor, we can substitute it back into the equation to find the equation that models the data.
Dragonflies = a * (2^day)
To determine the number of dragonflies on day 9, we can plug in the values into the equation.
Dragonflies at day 9 = a * (2^9)
Since we do not know the initial number of dragonflies (a), we cannot determine the exact value without that information. However, you can substitute any value of 'a' into the equation to find the corresponding number of dragonflies after 9 days.