Exponential Word Problems

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It describes growth or decay processes.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

Front

How do you calculate exponential growth?

Back

Exponential growth can be calculated using the formula A = Pe^(rt), where A is the amount after time t, P is the initial amount, e is the base of the natural logarithm, r is the growth rate, and t is time.

Front

How do you calculate exponential decay?

Back

Exponential decay can be calculated using the formula A = Pe^(-rt), where A is the amount after time t, P is the initial amount, e is the base of the natural logarithm, r is the decay rate, and t is time.

Front

What is the doubling time in exponential growth?

Back

The doubling time is the time required for a quantity to double in size or value. It can be calculated using the rule of 70: Doubling Time (in years) = 70 / growth rate (as a percentage).

Front

What is the half-life in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value. It is commonly used in radioactive decay and can be calculated using the formula: Half-life = ln(2) / decay rate.

Front

If a population of 1,000 increases by 20% each year, what will be the population after 3 years?

Back

Population after 3 years = 1000 * (1 + 0.20)^3 = 1,728.

Front

If a bacteria culture starts with 200 bacteria and doubles every 4 hours, how many bacteria will there be after 16 hours?

Back

After 16 hours, the population will be 200 * 2^(16/4) = 3,200 bacteria.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal time intervals, while exponential growth increases by a percentage of the current amount, leading to faster growth as the quantity increases.

Front

How do you solve an exponential equation?

Back

To solve an exponential equation, you can take the logarithm of both sides, which allows you to bring down the exponent and solve for the variable.