Question

A quantity $P$ is an exponential function of time $t .$ Use the given information about the function $P=P_{b} a^{t}$ to: (a) Find values for the parameters $a$ and $P_{0}$. (b) State the initial quantity and the percent rate of growth or decay. $P_{0} a^{3}=75 \quad$ and $\quad P_{0} a^{2}=50$

Name: Problem 20, Chapter 1: Applied Calculus
Uploaded: 2020-04-12T02:33:15-08:00
Duration: 52 s
Channel: Amrita Bhasin
Description: A quantity P is an exponential function of time t . Use the given information about the function P=Pb a^t to: (a) Find values for the parameters a and P0. (b) State the initial quantity and the percent rate of growth or decay. P0 a^3=75 and P0 a^2=50

   A quantity $P$ is an exponential function of time $t .$ Use the given information about the function $P=P_{b} a^{t}$ to:
(a) Find values for the parameters $a$ and $P_{0}$.
(b) State the initial quantity and the percent rate of growth or decay.
$P_{0} a^{3}=75 \quad$ and $\quad P_{0} a^{2}=50$

Applied Calculus

Deborah… 5th Edition

Chapter 1, Problem 20

Instant Answer

Solved by Expert Amrita Bhasin

04/12/2020

Step 1

We can divide the first equation by the second to get $a = \frac{75}{50} = 1.5$. Show more…

Show all steps

Thanks for your feedback!

A quantity $P$ is an exponential function of time $t .$ Use the given information about the function $P=P_{b} a^{t}$ to: (a) Find values for the parameters $a$ and $P_{0}$. (b) State the initial quantity and the percent rate of growth or decay. $P_{0} a^{3}=75 \quad$ and $\quad P_{0} a^{2}=50$

Play audio

Feedback

Amrita Bhasin and 89 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

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

Parameter Identification

Determining the parameters in an exponential function involves using given conditions at specific time points to set up equations that can be solved for the unknowns, such as the initial quantity P? and the exponential base a. This process may include dividing equations to eliminate one variable and isolate the other.

Percent Growth/Decay Rate

The percent rate of growth or decay is found by relating the exponential base a to a percentage. If a is greater than 1, the function represents growth, and if less than 1, decay. The rate is computed as (a - 1) multiplied by 100%, which gives the percentage change per time unit.

Exponential Functions

Exponential functions model a process in which the rate of change is proportional to the current value. They are typically expressed in the form P = P? * a^t, where P? is the initial quantity and a is the constant base representing the multiplication factor per time unit.

Please give Ace some feedback