Question

whats the sum of an infinite geometric series if \\(a_1 = 5\\) and \\(r = 1/3\\)?

a) 15
b) \\(15/2\\)
c) \\(25/2\\)
d) 30

question 14 (5 points)
a population of bacteria triples every hour. is this situation linear or exponential?

a) linear, because the function increases by a common difference
b) exponential, because the function grows by a common ratio
c) linear, because the function increases
d) exponential, because the function decreases

question 15 (5 points)
whats the sum of an infinite geometric series if \\(a_1 = 144\\) and \\(r = 1/4\\)?

a) 288
b) 192
c) 576
d) 252

Explanation:

Calculate the sum of the first infinite geometric series

$$ S = \frac{a_1}{1 - r} = \frac{5}{1 - \frac{1}{3}} = \frac{5}{\frac{2}{3}} = \frac{15}{2} $$

Determine the growth type of the bacteria population

$$
LATEXBLOCK0
$$

Calculate the sum of the second infinite geometric series

$$ S = \frac{a_1}{1 - r} = \frac{144}{1 - \frac{1}{4}} = \frac{144}{\frac{3}{4}} = 144 \times \frac{4}{3} = 48 \times 4 = 192 $$

Answer:

Question 1

• (A) 15
• (B) \(15/2\) (Correct answer)
• (C) \(25/2\)
• (D) 30

Question 2

• (A) Linear, because the function increases by a common difference
• (B) Exponential, because the function grows by a common ratio (Correct answer)
• (C) Linear, because the function increases
• (D) Exponential, because the function decreases

Question 3

• (A) 288
• (B) 192 (Correct answer)
• (C) 576
• (D) 252