Question

Suppose that $P^{\prime}(t)=0.15 P(t)$ represents a mathematical model for the growth of a certain cell culture, where $P(t)$ is the size of the culture (measured in millions of cells) at time $t$ (measured in hours). How fast is the culture growing at the time $t$ when the size of the culture reaches 2 million cells?

Name: Problem 39, Chapter 1: Advanced Engineering Mathematics
Uploaded: 2021-12-22T16:08:12-08:00
Duration: 1 min 9 s
Channel: Hast Aggarwal
Description: Suppose that P^'(t)=0.15 P(t) represents a mathematical model for the growth of a certain cell culture, where P(t) is the size of the culture (measured in millions of cells) at time t (measured in hours). How fast is the culture growing at the time t when the size of the culture reaches 2 million cells?

    Suppose that $P^{\prime}(t)=0.15 P(t)$ represents a mathematical model for the growth of a certain cell culture, where $P(t)$ is the size of the culture (measured in millions of cells) at time $t$ (measured in hours). How fast is the culture growing at the time $t$ when the size of the culture reaches 2 million cells?

Advanced Engineering Mathematics

Dennis G. Zill,… 5th Edition

Chapter 1, Problem 39

Instant Answer

Solved by Expert Hast Aggarwal

12/22/2021

Step 1

15 P(t)$. This is a differential equation that describes the rate of change of the size of the culture with respect to time. Show more…

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Suppose that $P^{\prime}(t)=0.15 P(t)$ represents a mathematical model for the growth of a certain cell culture, where $P(t)$ is the size of the culture (measured in millions of cells) at time $t$ (measured in hours). How fast is the culture growing at the time $t$ when the size of the culture reaches 2 million cells?

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Key Concepts

Exponential Growth

Exponential growth refers to the process where the rate of increase of a quantity is proportional to its current size. This leads to a situation where the quantity grows by a constant percentage over equal time intervals, resulting in a multiplicative, rather than additive, increase over time.

Rate of Change

In the context of growth models, the derivative represents the instantaneous rate of change of the quantity. It provides a measure of how fast the quantity (such as population) is increasing or decreasing at any given moment, based on its current value.

Differential Equations

Differential equations are mathematical equations that relate a function with its derivatives. They are used to model dynamic systems where changes depend on the current state, such as the rate of cell culture growth being directly proportional to its current size.

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