The number of plants in a terrarium is given by the function P(c) = -1.2c2 + 4c + 12 where c is the number of mg of plant food added to the terrarium. The amount of plant food that produces the highest number of plants is mg (round to the nearest hundredth).

15.33mg

Step-by-step 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).

answer: since the question is talking about growth you have to use the growth formula which is inital amount (1 + growth)^time

step-by-step explanation:

the intial amount is 1200, the growth is 4.8, and the time is 7. plug those numbers into the equation, also i think you have to change 4.8 into a percent. but, i have forgotton how to do that. if this is a online class go on to the lesson.