3a.3 Try It: Exponential Functions

Which function represents an exponential function?

• $f\left(x\right)=\frac{1}{2}x^2-5$

• $f\left(x\right)=5\cdot\left(\frac{1}{2}\right)^x$

• $f\left(x\right)=\frac{1}{2}x-5$

The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remaining teams t(n) is an exponential function of the number n of rounds already played.

• $t\left(n\right)\ =64\cdot\left(2\right)^n$

• $t\left(n\right)\ =64-\left(\frac{1}{2}\right)^n$

• $t\left(n\right)\ =\left(\frac{1}{2}\right)\cdot64^n$

• $t\left(n\right)\ =64\cdot\left(\frac{1}{2}\right)^n$

A pharmaceutical company is testing a new antibiotic. The number of bacteria present in a sample when the antibiotic is applied is 100,000. Each hour, the number of bacteria present decreases by half. The number of bacteria remaining r(n) is an exponential function of the number n of hours since the antibiotic was applied.

• $r\left(n\right)\ =\ 100,000\cdot\left(\frac{1}{2}\right)^n$

• $r\left(n\right)\ =\ 100,000-\left(\frac{1}{2}\right)^n$

• $r\left(n\right)\ =\ \frac{1}{2}\cdot\left(100,000\right)^n$

• $r\left(n\right)\ =\ 100,000\cdot\left(2\right)^n$

Find the common ratio: 4, -16, 64, -256, ...

• r = -4
• r = 2
• r = -2
• r = 4

Tags

CCSS.HSF.BF.A.2

What is the common ratio for the sequence:
28, 14, 7, 3.5...

• 2
• 1/2
• -14
• -7

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Which sequence is represented by the equation 2(7)^n-1 ?

• 7, 14, 28, 56...
• 2, 14, 98, 686...
• 2, 9, 16, 23...
• 7,9,11,13...

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

What is the explicit rule for the sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1
• a_n = 11x2
• a_n = 11(2)^n-1

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write an explicit rule for the general term of the sequence 5, 15, 45, . . . ?

• a_n = a_n-1 x 3
• a_n = 5(3)^n-1
• a_n = 3(5)^n-1
• a_n = 5 + (n-1)3

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Write the explicit formula for the geometric sequence.

• a_n = 4(3)^n-1
• a_n = 3(4)^n-1
• a_n = -4(3)^n-1
• a_n = 3(-4)^n-1

Tags

CCSS.HSF.BF.A.2

The rule for finding a_n of a geometric sequence is

a_n = 10(2)^n-1 _{What is the common ratio(r) of the sequence?}

• ²

• ¹⁰

• ²⁰

• 2ⁿ

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2