A type of plant is introduced into an ecosystem and quickly begins to take over. A scientist counts the number of plants after m months and develops the equation mc010-1.jpg to model the situation. Most recently, the scientist counted 138 plants. Assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants were first introduced?
The correct answer is 23.1
how about you provide the function, instead of naming a file we cannot see?
Is it p(t) = a*e^(kt)
with suitable values of a and k?
6.1 is incorrect
the answer is either 7.2 or 23.1
To determine how many months have passed since the plants were first introduced, we need to solve the equation mc010-1.jpg for m when the number of plants is 138.
The equation mc010-1.jpg represents exponential growth, where m is the number of months and 138 is the number of plants.
Therefore, we have:
138 = c(10^(-1))^m
First, we need to simplify the equation by evaluating (10^(-1))^m, which can be written as 1/10^m:
138 = c(1/10^m)
Next, we need to isolate m by dividing both sides of the equation by c:
138/c = 1/10^m
To further simplify, we can write 1/10^m as 10^(-m):
138/c = 10^(-m)
Now, we take the logarithm (base 10) of both sides of the equation to solve for m:
log(138/c) = log(10^(-m))
Using the property log(a^b) = b * log(a), we can rewrite the equation as:
log(138/c) = -m * log(10)
Since log(10) equals 1, the equation further simplifies to:
log(138/c) = -m
We can now solve for m by multiplying both sides of the equation by -1:
-m = -log(138/c)
Finally, we have:
m = log(138/c)
To find the value of m, you need to know the value of the constant c. Once you have that value, you can calculate m by substituting it into the equation m = log(138/c).