Exponential and Logarithmic Functions

What is the equation of the horizontal asymptote of the function

y = 2(0.3)^{x - 1} - 4?

• y = -4

• y = 2

• y = 0.3

• y = 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

Which function does not model exponential decay?

• y = 3/4 e^-3x

• y = 4/3 e ^-3x

• y = 4 e^-3x

• y = 4 e^3x

Tags

CCSS.HSF.LE.A.1

Which expression is equivalent to x?

• $\log x$

• $\log2^x$

• $\log10^x$

• $\log100^x$

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Which of the following is an equivalent expression for  $2\log_43+\log_42?$  

•  $2\log_46$  

•  $\log_46$  

•  $\log_412$  

•  $\log_418$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Which of the following is not equivalent to  $\log_58?$  

•  $\log_5\left(\frac{16}{2}\right)$  

•  $2\log_54$  

•  $3\log_52$  

•  $\log_54+\log_52$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

What is the range of this exponential function?
 $y=-3\cdot5^{\left(x+3\right)\ }$  

•  $\left(-\infty,\ 0\right)$  

• all real numbers

•  $\left(-\infty,3\right)$  

•  $\left(0,\infty\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.LE.B.5

A town doubles its size every 33 years. If the population is currently 6,000, what will the population be in 66 years?

• 12,000

• 24,000

• 198,000

• 396,000

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Condense into single logarithm.

18log₉a + 6log₉b

• log₉a¹⁸b⁶

• log_a18 + log_b6 = 9

• log₉(a¹⁸ + b⁶)

• log_b9(a¹⁸ + log₆)

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand.

log₄a⁶b⁵

• 6log₄a - 5log₄b

• log₄a + log₄b = 30

• 4log₆a + 4log₅b

• 6log₄a + 5log₄b

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

True or False?

log_xx^x = x

• True

• False

Tags

CCSS.HSF.BF.B.5