Unit 2A Review

The first term in a geometric sequence is g₁ = 5. For n > 2, the terms of a geometric sequence given by g_n = 3 * g_{(n - 1)}. For which of the following functions is g_n = f(n) for positive integer values of n?

• f(x) = 3 * 5ⁿ

• f(x) = 3 * 5^{n - 1}

• f(x) = 5 * 3ⁿ

• f(x) = 5 * 3^{n - 1}

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.3

The first term of a geometric sequence is 5. The 8th term is 10,935. What is the 3rd term of the sequence?

• 30
• 100
• 15
• 45

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

The number of bacteria in a dish is 1120 at time t = 0 hours. The number of bacteria in the dish doubles every 3 hours. If the function B gives the number of bacteria in the dish at time t hours for t > 0, which of the following could define b(t)?

• B(t) = 1120 * 2^t/2

• B(t) = 1120 + 2^t/2

• B(t) = 1120 * 3^t/3

• B(t) = 1120 * 2^t/3

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Mr. Rogers drops a golf ball from the top of the high school at a height of 20 feet. The ball repeat bounces, and the maximum height of the ball after each bounce is 18% less than the previous maximum height. Which of the following arguments is correct regarding a sequence that can be used to model the successive maximum heights, in feet?

• An arithmetic sequence is appropriate because each successive height would be found by subtracting 18 from the previous height.

• An arithmetic sequence is appropriate because each successive height would be found by multiplying 0.82 from the previous height.

• An geometric sequence is appropriate because each successive height would be found by multiplying 0.82 from the previous height.

• An geometric sequence is appropriate because each successive height would be found by subtracting 18 from the previous height.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

The function g is given by g(x) = 4 * 2^{3 + x}. The function g can also be expressed as which of the following?

• 32 + 2^x

• 32 * 2^x

• 32 + 8^x

• 512 * 8^x

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.C.8

• A(t) = 200πt

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

If f(x) = x + 2 and g(x) = ln(x), what is g(f(x))?

• ln(x + 1)
• x + 2

• ln(x) + 2
• ln(x + 2)

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

In the xy-plane, the graphs of the linear function L and the exponential function E both pass through the points (0,2) and (1, 6). The function f is given by f(x) = L(x) - E(x). What is the maximum value of f?

• 0.007

• 0.172

• 0.540

• 1.002

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

The function h is given by h(x) = a * b^-x, where a < 0 and b > 1. Which of the following describes h and its graph in the xy-plane?

• h is increasing, and the graph of h is concave down

• h is increasing and the graph of h is concave up

• h is decreasing and the graph of h is concave down

• h is decreasing and the graph of h is concave up

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7