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Rates of Change of Exponential Functions

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Wize High School Grade 12 Pre-Calculus Textbook > Rates of Change

Rates of Change of Exponential Functions

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Practice: Rates of Change of Exponential Functions

The population of a colony of ants increases 3-fold every 2 weeks. If the population of ants starts with 43, then:
More Rates of Change of Exponential Functions Questions:
Rates of Change
The instantaneous rate of change for f(x)=2xf(x)=2^{x} is 32\dfrac{3}{2}.
If h=0.001h=0.001, what is xx?
Rates of Change
The population of flies is given by P(t)=15(5)t/4P(t)=15(5)^{t/4}, where tt is in weeks.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
If the instantaneous rate of change for the function f(t)=−6(0.45)t2f(t)=-6(0.45)^{\frac{t}{2}} is 55, what is tt? Let h=0.001h=0.001.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
If the instantaneous rate of change for the function f(t)=4(1.75)t2f(t)=4(1.75)^{\frac{t}{2}} is 1313, what is tt? Let h=0.001h=0.001.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
When light passes through water, it loses 10%10\% of its intensity every 2525 meters.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
A ball is bounced and it obtains a maximum height of 8 meters. Every time the ball hits the ground, it reaches 80%80\% of its original height.
Rates of Change of Exponential Functions
Practice: Rates of Change of Exponential Functions
A car depreciates in value once it is driven off the lot. Matija is looking into buying a new car worth $60,000\$60,000 and the car depreciates in value by 3%3\% annually.