Exponential Functions (correct thru #17)

Values of the terms of a geometric sequence g_n are graphed in the figure. Which of the following is an expression for the nth term of the geometric sequence?

Tags

CCSS.HSF.BF.A.2

A large theater has rows of seats arranged in a way that the number of seats in each consecutive row form an arithmetic sequence. If the fourth row contains 30 seats and the eighth row contains 54 seats, which of the following gives the number of seats in the tenth row?

• 60

• 66

• 75

• 78

Tags

CCSS.HSF.BF.A.2

The table gives values of the sequence s_n at selected values of n. Which of the following statements about s_n is true?

• s_n could be an arithmetic sequence, because successive terms have a constant difference.

• s_n could be an arithmetic sequence, because successive terms have constant proportional change.

• s_n could be a geometric sequence, because successive terms have a constant difference.

• s_n could be a geometric sequence, because successive terms have constant proportional change.

Tags

CCSS.HSF.BF.A.2

Let g_n be a geometric sequence with g₁ = 3 and g₄ = 24. Which of the following is the value of g₃?

• 6

• 8

• 12

• 17

Tags

CCSS.HSF.BF.A.2

[CALC] Fearing a new computer virus, a security company performs a simulation to predict the number of computers that might be affected by the virus. The number of infected computers can be modeled by a geometric sequence, where the first day of the simulation is day 1. On day 6, the virus had infected 750 computers, and on day 10 the virus had infected 3200 computers. To the nearest whole number, how many computers had been infected by the virus on day 14 based on the simulation?

• 5,650

• 5,717

• 13,653

• 120,329

Tags

CCSS.HSF.BF.A.2

• lim_{x→∞} g(x) = 0 and lim_{x→−∞} g(x) = −∞

• lim_{x→∞} g(x) = −∞ and lim_{x→−∞} g(x) = 0

• lim_{x→∞} g(x) = 0 and lim_{x→−∞} g(x) = 0

• lim_{x→∞} g(x) = ∞ and lim_{x→−∞} g(x) = 0

Tags

CCSS.HSF-IF.C.7E

• lim_{x→∞} f(x) = 0 and lim_{x→−∞} f(x) = −∞

• lim_{x→∞} f(x) = −∞ and lim_{x→−∞} f(x) = 0

• lim_{x→∞} f(x) = 0 and lim_{x→−∞} f(x) = ∞

• lim_{x→∞} f(x) = ∞ and lim_{x→−∞} f(x) = 0

Tags

CCSS.HSF-IF.C.7E

• f demonstrates exponential decay because a > 0 and 0 < b < 1.

• f demonstrates exponential decay because a > 0 and b > 1.

• f demonstrates exponential growth because a > 0 and 0 < b < 1.

• f demonstrates exponential growth because a > 0 and b > 1.

Tags

CCSS.HSF.LE.A.2

• f is always increasing, and the graph of f is always concave up.

• f is always increasing, and the graph of f is always concave down.

• f is always decreasing, and the graph of f is always concave up.

• f is always decreasing, and the graph of f is always concave down.

Tags

CCSS.HSF-IF.C.7E

The figure shows a portion of the graph of a function h. Which of the following conclusions is possible for h?

• h is logarithmic because the output values are proportional over equal-length input-value intervals.

• h is logarithmic because the input values are proportional over equal-length output-value intervals.

• h is exponential because the output values are proportional over equal-length input-value intervals.

• h is exponential because the input values are proportional over equal-length output-value intervals.

Tags

CCSS.HSF-IF.C.7E