Exponential Growth

Front

What is exponential growth?

Back

Exponential growth is a process where the quantity increases at a rate proportional to its current value, leading to faster and faster increases over time.

Front

What is the formula for exponential growth?

Back

The formula is: N(t) = N0 * e^(rt), where N(t) is the quantity at time t, N0 is the initial quantity, r is the growth rate, and e is the base of the natural logarithm.

Front

If a population of 4,000 mosquitoes grows at a rate of 25% per month, how many will there be after 4 months?

Back

9766 mosquitoes.

Front

What is the growth factor in exponential growth?

Back

The growth factor is 1 + r, where r is the growth rate expressed as a decimal.

Front

How do you convert a percentage growth rate to a decimal?

Back

Divide the percentage by 100. For example, 25% becomes 0.25.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage of the current amount.

Front

What does the term 'doubling time' refer to in exponential growth?

Back

Doubling time is the period it takes for a quantity to double in size at a constant growth rate.

Front

If the attendance at a museum is 250 and increases by 3% each month, how many will attend after one year?

Back

356 people.

Front

What type of function represents exponential growth?

Back

Exponential functions, typically in the form y = ab^x, where a is the initial amount, b is the growth factor, and x is time.

Front

What is the equation for a population that doubles every month?

Back

y = N0 * 2^x, where N0 is the initial population and x is the number of months.