Answer:
15.33mg
Explanation:
Given the number of plants in a terrarium is given by the function
P(c) = -1.2c^2 + 4c + 12
At the hihest number of plants produced, dP(c)/dc = 0
dP(c)/dc = --2.4c + 4
0 = -2.4c + 4
2.4c = 4
c = 4/2.4
c = 1.67
To get the highest number of plant produced, we will substitute c = 1.67 into the original function
P(c) = -1.2c^2 + 4c + 12
P(1.67) = -1.2(1.67)^2 + 4(1.67) + 12
P(1.67) = -3.34668 + 18.68
P(1.67) = 15.33332
Hence the amount of plant food that produces the highest number of plants is 15.33mg (round to the nearest hundredth).