Question

Suppose a lake contains blue and green algae. The blue algae has an initial mass of 20 kg and doubles its mass every hour. The green algae has an initial mass of 160 kg and grows at a constant rate of 0.20 kg per minute.
Which algae has a larger mass at 3 hours, in kilograms?
A) The blue algae has 12 kg more mass at 3 hours.
B) The green algae has 12 kg more mass at 3 hours.
C) The blue algae has 36 kg more mass at 3 hours.
D) The green algae has 36 kg more mass at 3 hours.

Which algae has a larger mass at 4 hours, in kilograms?
A) The blue algae has 56 kg more mass at 4 hours.
B) The green algae has 56 kg more mass at 4 hours.
C) The blue algae has 112 kg more mass at 4 hours.
D) The green algae has 112 kg more mass at 4 hours

Answer 1

Answer:

1) D

2) C

Step-by-step explanation:

1. The blue algae has an initial mass of 20 kg and doubles its mass every hour. Then after t hours, the mass of blue algae is

$M_1=20\cdot 2^t\ kg$

2. The green algae has an initial mass of 160 kg and grows at a constant rate of 0.20 kg per minute. Then after t hours (60t minutes), the mass of green algae is

$M_2=160+0.20\cdot 60t\ kg.$

Part I) At t=3:

$M_1=20\cdot 2^3=160\ kg,\\ \\M_2=160+0.2\cdot 60\cdot 3=160+36=196\ kg.$

The mass of green algae has 196-160=36 kg more mass at 3 hours.

Part II) At t=4:

$M_1=20\cdot 2^4=320\ kg,\\ \\M_2=160+0.2\cdot 60\cdot 4=160+48=208\ kg.$

The blue algae has 320-208=112 kg more mass at 4 hours.