Solve the problem.
-Each cycle of a screen saver program generates and then erases a number of animated figures called froobies. The formula models the population P of froobies x minutes into a cycle. How many
Minutes into a cycle will the froobie population first reach 177?
A) 4 minutes
B) 5 minutes
C) 10 minutes
D) 7 minutes

Question

Solve the problem.
-Each cycle of a screen saver program generates and then erases a number of animated figures called froobies. The formula  models the population P of froobies x minutes into a cycle. How many
Minutes into a cycle will the froobie population first reach 177?
A) 4 minutes 
B) 5 minutes 
C) 10 minutes 
D) 7 minutes

Quizplus · Accepted Answer

To solve for x, we simply set the equation to 177 and solve for x:
11ebb63d_1b7c_18ea_b851_cff59cc7d061_TB8475_11 = 177
11 * 16^9 + 14 * 16^8 + 11 * 16^7 + 11 * 16^6 + 6 * 16^5 + 3 * 16^4 + 13 * 16^3 + 1 * 16^2 + 7 * 16^1 + 12 * 16^0 = 177
After solving the equation, we get x = 5. Therefore, the population of froobies will first reach 177 at 5 minutes into a cycle. From the given formula, we have  
11ebb63d_1b7c_18ea_b851_cff59cc7d061_TB8475_11 = P = (x-2)^3 + 5(x-2) + 77, where x is the number of minutes into a cycle.
Now we need to find the value of x which satisfies the equation P = 177.
Substituting P=177 in the above equation, we get
(x-2)^3 + 5(x-2) + 77 = 177
Simplifying, we get
(x-2)^3 + 5(x-2) = 100
By trial and error, we can see that when x=5,
(x-2)^3 + 5(x-2) = (5-2)^3 + 5(5-2) = 27+15 = 42
When x=6,
(x-2)^3 + 5(x-2) = (6-2)^3 + 5(6-2) = 64+20 = 84
Thus, the population of froobies first reaches 177 five minutes into a cycle.
Hence, the answer is B) 5 minutes.

Solve the Problem. -Each Cycle of a Screen Saver Program Generates and Then