Use the exponential decay model, A=A0 e^k t, Round answers...

Use the exponential decay model, $A=A_{0} e^{k t},$ Round answers to one decimal place.a growth rate $k$ to double. Express each answer to the nearest whole year. The growth model $A=112.5 e^{0.012 t}$ describes Mexico's population, $A,$ in millions, $t$ years after 2010 a. What is Mexico's growth rate? b. How long will it take Mexico to double its population?

Use the exponential decay model, $A=A_{0} e^{k t},$ Round answers to one decimal place.a growth rate $k$ to double. Express each answer to the nearest whole year.
The growth model $A=112.5 e^{0.012 t}$ describes Mexico's population, $A,$ in millions, $t$ years after 2010
a. What is Mexico's growth rate?
b. How long will it take Mexico to double its population?

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 and Decay Models

These models describe processes in which a quantity changes at a rate proportional to its current value, and are typically represented by the formula A = A0 e^(kt). In this equation, A0 is the initial amount, k is the constant that represents the rate of growth (if positive) or decay (if negative), and t represents time.

Growth Rate

The growth rate, denoted by k in the exponential model, is a key parameter that determines how quickly the quantity increases or decreases over time. It provides a measure of the instantaneous rate at which the population or quantity is growing relative to its current size.

Doubling Time

Doubling time is the period required for a growing quantity to become twice its original amount. In the context of exponential growth, it can be calculated by setting the equation A = A0 e^(kt) equal to 2A0 and solving for t using logarithms, typically yielding the formula t = ln(2)/k.

Natural Logarithms

Natural logarithms are used to solve equations where the unknown variable appears in the exponent. They are crucial in isolating the time variable in exponential growth and decay problems, allowing for the calculation of quantities such as doubling time.

Transcript

Please give Ace some feedback