Word Problems #3

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for a population to increase by a certain percentage each year?

Back

It means that each year, the population grows by that percentage of the current population. For example, a 4% increase means the population grows by 4% of its current size every year.

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, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does the term 'model' mean in mathematics?

Back

In mathematics, a model is a representation of a real-world situation using mathematical concepts and equations to describe relationships between variables.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

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 do you interpret the slope in a linear equation?

Back

The slope in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

Front

What is a percentage increase?

Back

A percentage increase is a way to express how much a quantity has grown relative to its original amount, calculated as (new value - original value) / original value * 100%.

Front

What does 't' represent in the population model P=6191(1.04)^t?

Back

In the model P=6191(1.04)^t, 't' represents the number of years since 1990.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, leading to faster growth over time, while linear growth increases by a constant amount.