CIA 2 Review - Exponential Functions

Front

What is the formula for calculating the present value of an investment that depreciates over time?

Back

The present value (PV) can be calculated using the formula: PV = P(1 - r)^t, where P is the initial value, r is the rate of depreciation, and t is the time in years.

Front

What does the equation P=150(2)^t represent in the context of population growth?

Back

This equation represents exponential growth, where P is the population at time t, 150 is the initial population, and 2 is the growth factor (doubling every time unit).

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Back

Front

What is the relationship between the base and the exponent in exponential functions?

Back

In exponential functions, the base is a constant that determines the growth rate, while the exponent represents the time or number of periods.

Front

What is the formula for calculating future population given a current population and growth rate?

Back

The future population can be calculated using the formula: Future Population = Current Population * (1 + r)^t, where r is the growth rate and t is the number of years.

Front

Back

x = 2.

Front

How do you express 36 as a power of 6?

Back

36 can be expressed as 6^2.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is: N(t) = N_0 * e^{-kt}, where N_0 is the initial quantity, k is the decay constant, and t is time.

Front

What does a 3% annual increase in population mean in terms of exponential growth?

Back

A 3% annual increase means that each year, the population is multiplied by 1.03, representing a growth factor of 1.03.

Front

What is the initial value in the equation P=150(2)^t?

Back

The initial value is 150, which represents the population at time t=0.