Unit 2 Exponential and Logarithmic Functions

Classify
 f(x)=-3(1.75)^x-4+6

• Exponential Growth

• Exponential Decay

Answer explanation

The function f(x) = -3(1.75)^(x-4) + 6 has a base of 1.75, which is greater than 1. This indicates exponential growth, as the function increases as x increases.

Tags

CCSS.HSF-IF.C.8B

What function is present? 

• Absolute Value

• Exponential Decay

• Linear Equation

• Exponential Growth

Answer explanation

The function identified is Exponential Decay, which describes a process where a quantity decreases at a rate proportional to its current value, unlike Linear Equation or Exponential Growth, which represent different behaviors.

Tags

CCSS.HSF-IF.C.7E

Convert between logarithmic and exponential form

[Click on the image if you need to make it larger]

• A

• B

• C

• D

Answer explanation

To convert from logarithmic to exponential form, use the definition: if log_b(a) = c, then b^c = a. The correct choice A correctly represents this conversion.

Tags

CCSS.HSF.BF.B.5

Condense

• A

• B

• C

• D

Answer explanation

The correct answer is B because it effectively captures the essence of the term 'condense', which means to make something denser or more concise. Options A, C, and D do not align with this definition.

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Condense

• A

• B

• C

• D

Answer explanation

The correct answer is C because it effectively captures the essence of the term 'condense', which means to make something denser or more concise. Options A, B, and D do not align with this definition.

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

• log (a⁵ + b²⁵)
• log (a⁵ − b²⁵)
• log (ab²⁵)
• log (a⁵/b²⁵)

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Answer explanation

Using the properties of logarithms, we can combine the logs: \log_2\left(\frac{x^2+2x}{x}\right)=3. This simplifies to \log_2\left(x+2\right)=3, leading to x+2=8. Thus, x=6. However, x=0 is also a solution since it satisfies the original equation.

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

Answer explanation

The bacteria die at a rate of 30% each year, meaning 70% survive. The equation representing this decay is y=5000(0.7)^x, where 5000 is the initial amount and 0.7 represents the remaining percentage.

Tags

CCSS.HSF.LE.A.2

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

• $0.29

• $2,900,000,000

• $46,704.79

• $145,000

Answer explanation

To find the car's value in 5 years, use the formula: Future Value = Present Value * (1 + rate)^years. Here, it’s $29,000 * (1 + 0.10)^5 = $46,704.79. Thus, the correct answer is $46,704.79.

Tags

CCSS.HSF.BF.A.2

Answer explanation

To convert the exponential equation e^3 = x to logarithmic form, we use the definition of logarithms. This gives us ln(x) = 3, which matches the correct answer choice.

Tags

CCSS.HSF.BF.B.5