Exponential Growth and Decay

Front

What is the general form of an exponential growth function?

Back

y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time in years.

Front

What is the general form of an exponential decay function?

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time in years.

Front

How do you calculate the population after a certain number of years using exponential decay?

Back

Use the formula: P = P0(1 - r)^t, where P0 is the initial population, r is the decay rate, and t is the number of years.

Front

What does a growth rate of 35% per year mean in terms of an exponential function?

Back

It means that the function increases by 35% of its current value each year, represented as y = a(1.35)^x.

Front

If a population decreases by 6% per year, what is the decay factor?

Back

The decay factor is 1 - 0.06 = 0.94.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300.

Front

How do you find the value of an asset after a certain number of years with 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 the number of years.

Front

What is the value of an asset worth $35,000 after 8 years with a depreciation rate of 5%?

Back

The value after 8 years is approximately $23,219.72.

Front

What is the difference between exponential growth and exponential decay?

Back

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

Front

How do you express a 5% depreciation rate in decimal form?

Back

5% as a decimal is 0.05.