U5 Determine the Equation from Context

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is P = P0(1 + r)^t, where P0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is V = V0(1 - r)^t, where V0 is the initial value, r is the decay rate, and t is time.

Front

How do you calculate the population after t years with an annual growth rate of 8%?

Back

Use the formula P = P0(1.08)^t, where P0 is the current population.

Front

What does 'compounded annually' mean in the context of investments?

Back

'Compounded annually' means that the interest earned is added to the principal once a year, and future interest calculations are based on the new total.

Front

If an investment of $1000 grows at a rate of 6% annually, what will it be worth after 3 years?

Back

A = 1000(1.06)^3 = $1,191.016.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function indicates the growth or decay factor; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you represent a quantity that triples every day?

Back

Use the equation S = S0(3)^t, where S0 is the initial quantity.

Front

What is the formula for calculating the future value of a depreciating asset?

Back

The formula is V = V0(1 - r)^t, where V0 is the initial value and r is the depreciation rate.

Front

If a car's value is $20,000 and it depreciates by 15% annually, what is its value after 2 years?

Back

V = 20000(0.85)^2 = $12,250.

Front

What does it mean if a population increases by 8% annually?

Back

It means that each year, the population grows by 8% of its current size.