10.2 Applications

Front

What is the formula to estimate population decline over time?

Back

The formula is P = P0(1 - r)^t, where P0 is the initial population, r is the rate of decline, and t is the time in years.

Front

How do you represent a culture of bacteria that dies by a certain percentage each year?

Back

The equation is y = P0(1 - r)^t, where P0 is the initial number of bacteria, r is the death rate, and t is time in years.

Front

What does the equation y = a(1 - r)^x represent?

Back

It represents exponential decay, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

What is the half-life of a substance?

Back

The half-life is the time required for a quantity to reduce to half its initial value.

Front

How do you calculate the value of an asset after depreciation?

Back

Use the formula V = P(1 - r)^t, where V is the value after t years, P is the initial value, r is the depreciation rate, and t is time.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth increases over time, while exponential decay decreases over time.

Front

What is the formula for exponential growth?

Back

The formula is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

If a sample of Uranium loses half its mass each year, what is the equation?

Back

The equation is y = 78(0.5)^x, where 78 is the initial mass and x is the number of years.

Front

How do you model the depreciation of a vehicle?

Back

The model is y = P(1 - r)^t, where P is the initial price, r is the depreciation rate, and t is the number of years.

Front

What is the significance of the decay constant in exponential decay?

Back

The decay constant indicates the rate at which a quantity decreases over time.