Exponential Function Word problems Part 2

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(t) = a * b^t, where 'a' is a constant, 'b' is the base (a positive real number), and 't' is the exponent, representing time or another variable.

Front

How do you calculate the remaining amount of a substance after a percentage decrease?

Back

To calculate the remaining amount after a percentage decrease, use the formula: Remaining Amount = Initial Amount * (1 - Percentage Decrease) ^ t, where 't' is the time period.

Front

What does a growth rate of 4% per year mean in terms of population?

Back

A growth rate of 4% per year means that the population increases by 4% of its current size each year.

Front

How do you determine the time it takes for a value to decrease to a certain amount with a fixed percentage decrease?

Back

To determine the time, use the formula: t = log(final amount / initial amount) / log(1 - percentage decrease).

Front

What is the doubling time in exponential growth?

Back

The doubling time is the period it takes for a quantity to double in size, which can be estimated using the rule of 70: Doubling Time (in years) = 70 / growth rate (in %).

Front

If a population grows at 25% per month, how do you calculate the population after several months?

Back

Use the formula: Future Population = Initial Population * (1 + growth rate) ^ number of months.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is: N(t) = N0 * e^(-kt), where N0 is the initial quantity, k is the decay constant, and t is time.

Front

How do you find the percentage increase from one value to another?

Back

Percentage Increase = ((New Value - Original Value) / Original Value) * 100%.

Front

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

Back

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

Front

How can you model population growth using an exponential function?

Back

Population growth can be modeled using the formula P(t) = P0 * e^(rt), where P0 is the initial population, r is the growth rate, and t is time.