Question

Match each situation to its corresponding expression.

150(0.4)^n
2,500 (1.11)^n
150(0.6)^n
2,500(0.11)^n

In a singing competition, there are
150 participants. At the end of each round, 40% of the participants are
eliminated. How many participants
are left after n rounds?

At the start of an experiment, there are 2,500 bacteria in a colony. The colony grows at a rate of 11% every hour. What will be the number of bacteria in the colony after n hours?

Answer 1

• (c) 150(0.6^n)
• (b) 2500(1.11^n)

Explanation:

Exponential growth or decay can be modeled by the exponential function ...

f(n) = a×b^n

where 'a' is the initial value, and 'b' is the growth factor. The growth factor is ...

b = 1 +r

where r is the growth rate. If decay is involved, the sign of r will be negative.

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competition

If 40% of the participants are eliminated each round, then the growth rate per round is -40% = -0.40, and the growth factor is ...

b = 1 -0.40 = 0.60

The initial number of participants is 150, so the number remaining after n rounds is ...

f(n) = 150×0.60^n . . . . . . matches the 3rd choice

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bacteria

The growth rate of 11% per hour means the growth factor is ...

b = 1 +11% = 1.11

The initial population is 2500, so the population after n hours is ...

f(n) = 2500×1.11^n . . . . . . matches the 2nd choice