SOLUTION: y = t^2 + 4t + 10 Which of the following scenarios could be modeled by y in the equation above, where t represents time? A. A population of ladybugs that doubles every four w

Question 1183474: y = t^2 + 4t + 10
Which of the following scenarios could be modeled by y in the equation above, where t represents time?
A. A population of ladybugs that doubles every four weeks.
B. The height of a rock that is dropped off a ten-foot cliff.
C. The height of a hot air balloon that accelerates as it rises.
D. The value of an investment that increases by 5% every quarter.

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
y = t^2 + 4t + 10
Which of the following scenarios could be modeled by y in the equation above, where t represents time?
A. A population of ladybugs that doubles every four weeks.
B. The height of a rock that is dropped off a ten-foot cliff.
C. The height of a hot air balloon that accelerates as it rises.
D. The value of an investment that increases by 5% every quarter.
~~~~~~~~~~~~

(A)  The model for this scenario is an exponential function  y = a*2^(t/4),  where "t" is the time, in weeks,

     which is not the given equation.




(B)  The model for this scenario is  y = , where g is the gravity acceleration and t is the time,
 
     which is not the given equation.




(C)  It can be modeled by the given equation.

     The buoyancy force provides the acceleration.




(D)  The model for this scenario is  FV = , where P is the principal, n is the number of quarters

     and (1+r) id the quarterly growth multiplicative factor.

     This equation is of different form comparing with the given equation.

ANSWER. The only possible version is option (C).

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Solved and explained.

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