Understanding Linear and Exponential Functions

The video tutorial explains the difference between linear and exponential functions using examples. It starts with a problem about a calf's weight increasing by 5% weekly, demonstrating exponential growth. The tutorial further explores other scenarios, such as a coin's value increasing by 10% annually and a car's value decreasing by a fixed amount, to illustrate linear and exponential changes. The key takeaway is understanding how to identify and differentiate between linear and exponential growth in various contexts.

What is the initial weight of the newborn calf?

• 30 kilograms

• 40 kilograms

• 50 kilograms

• 60 kilograms

If the calf's weight increased by a fixed amount each week, what type of function would it be?

• Exponential

• Logarithmic

• Quadratic

• Linear

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CCSS.HSF.BF.A.2

By what percentage does the calf's weight increase each week?

• 3%

• 5%

• 2%

• 4%

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CCSS.HSF.LE.A.2

What is the formula for the calf's weight after t weeks?

• 40 * t^1.05

• 40 + 5t

• 40 * 1.05^t

• 40 * 0.05^t

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CCSS.HSF-LE.A.1A

Why is the calf's weight increase considered exponential?

• Because it remains constant

• Because it decreases over time

• Because it increases by a percentage

• Because it increases by a fixed amount

If a coin's value increases by 10% each year, what type of function describes its value?

• Linear

• Exponential

• Quadratic

• Logarithmic

If a car's value decreases by 10,000 pesos each year, what type of function describes its value?

• Exponential

• Quadratic

• Logarithmic

• Linear

The number of wild hogs in Arkansas increases by a factor of 3 every 5 years. What type of function is this?

• Linear

• Exponential

• Logarithmic

• Quadratic

If you earn $50 in tips every day you work, what type of function describes your earnings?

• Exponential

• Quadratic

• Linear

• Logarithmic

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CCSS.8.F.A.3

Which of the following scenarios describes a linear function?

• A population doubling every year

• A tree growing 10% taller each year

• A car losing 10,000 pesos in value each year

• A bank account growing by 5% interest annually

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CCSS.8.F.A.3