Gross Domestic Product In Exercise 47 of the previous sec-...

Gross Domestic Product In Exercise 47 of the previous sec- tion, the Gross Domestic Product (GDP) for the United States was modeled by the exponential function $$f(t)=92(1.0657)^{t},$$ where $f(t)$ was the GDP (in billions of current dollars) and $t$ was the number of years since $1930 .$ In what year will the GDP reach $29,930 ?$

Gross Domestic Product In Exercise 47 of the previous sec-
tion, the Gross Domestic Product (GDP) for the United States
was modeled by the exponential function
$$f(t)=92(1.0657)^{t},$$
where $f(t)$ was the GDP (in billions of current dollars) and $t$
was the number of years since $1930 .$ In what year will the GDP
reach $29,930 ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Exponential Growth Model

An exponential growth model uses an exponential function to describe processes that increase by a constant multiplicative rate over time. This type of model is particularly useful for representing phenomena where the growth is proportional to the current amount, leading to faster increases as the quantity becomes larger.

Gross Domestic Product (GDP)

Gross Domestic Product is a measure of the economic performance of a country, representing the total value of all goods and services produced over a specific period. It serves as a primary indicator of economic health and is often used to compare the economic productivity of different countries or regions over time.

Logarithms in Exponential Equations

Logarithms are a mathematical tool used to solve equations where the variable appears as an exponent. By taking the logarithm of both sides of an exponential equation, one can bring the exponent down and isolate the variable, making it possible to solve for the time or rate in contexts such as determining when a growing quantity will reach a specific value.

Transcript

Please give Ace some feedback