Help needed For Math?

1. A scientist is doing an experiment with a chemical that has a half- life of 11 days. How much of the chemical will be remaining after 40 days if there were 300 grams at the begining of his lab?

2. y= 2/3x^3 -2x^2 -30x
For what values in the domain is the above function increasing?
For what values in the domain is the above function decreasing?

3. A real estate office handles 50 apartment units. when the rent is $270 permonth all units are occupied. However, on the average, for each $15 increase in rent , one unit becomes vacant. also, each occupied unit requires an average of $18 per month for service and repairs. Write an equation that describes the profit in the given situation .

1.) (ln 2)/11 = k
k =.063
y = 300e^[-.063(40)]
y = 24.1379 grams

2.) This question doesn't really make sense. I assume you meant the function as a whole.

find the derivative 2x虏 - 4x - 30
find the roots 2x虏 - 4x - 30 = 0
x虏 - 2x - 15 = 0
(x - 5)(x + 3) = 0
x = {5, -3}
Now test a value on each of the intervals negative infinity to negative 3, negative 3 to 5, and 5 to infinity.
If the sign of the value is positive, the slope is positive and the function is increasing, otherwise it is decreasing.

In this case, the function is increasing on the interval (-鈭?-3), decreasing (-2, 5), and increasing (5, 鈭?

3.) let r be revenue and i be each $15 increase

r = -15i虏 +481i +12600

That last one was really hard

1. A scientist is doing an experiment with a chemical that has a half- life of 11 days. How much of the chemical will be remaining after 40 days if there were 300 grams at the begining of his lab?
Mass = 300 (1/2)^(40/11) = 24.12 grams

2. y= 2/3x^3 -2x^2 -30x
y' = 2x^2 -4x -30
y' = 2(x^2 -2x -15)
y' = 2(x-5)(x+3)
y' > 0 for x<-3
y' < 0 for x>-3 and x<5
y' > 0 for x<5

3. A real estate office handles 50 apartment units. when the rent is $270 per month all units are occupied. However, on the average, for each $15 increase in rent , one unit becomes vacant. also, each occupied unit requires an average of $18 per month for service and repairs. Write an equation that describes the profit in the given situation .
Let X be the number of increases
Profit(units) = (50-X)*(270+15X)-18(50-X)