Question

A population of bacteria is growing according to the equation $P(t)=1600 e^{0.21 t}$, with $t$ measured in years. Estimate when the population will exceed $7569 .$

Name: Problem 33, Chapter 4: Precalculus: An Investigation of Functions
Uploaded: 2021-08-17T07:13:24-08:00
Duration: 2 min 54 s
Channel: Sreeraj P
Description: A population of bacteria is growing according to the equation P(t)=1600 e^0.21 t, with t measured in years. Estimate when the population will exceed 7569 .

   A population of bacteria is growing according to the equation $P(t)=1600 e^{0.21 t}$, with $t$ measured in years. Estimate when the population will exceed $7569 .$

Precalculus: An Investigation of Functions

David Lippman 2017 Edition

Chapter 4, Problem 33

Instant Answer

Solved by Expert Sreeraj P

08/17/2021

Step 1

21 t}$ and we need to find the time $t$ when the population exceeds $7569$. So, we set $P(t)$ to $7569$ and solve for $t$: \[7569 = 1600 e^{0.21 t}\] Show more…

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A population of bacteria is growing according to the equation $P(t)=1600 e^{0.21 t}$, with $t$ measured in years. Estimate when the population will exceed $7569 .$

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Key Concepts

Exponential Growth

Exponential growth describes processes in which a quantity increases by a fixed percentage or factor over equal time intervals. It is a key concept in modeling populations, financial investments, and many natural phenomena where the rate of increase is proportional to the current amount.

Exponential Functions

Exponential functions have the form f(t) = A * e^(kt), where A is the initial value and k is the constant growth (or decay) rate. These functions model situations where changes occur continuously and multiplicatively over time.

Logarithms

Logarithms are the inverse operations of exponentiation and are used to solve equations where the unknown appears in the exponent. They allow us to isolate the variable in exponential equations and inequalities, such as determining the time required for a population to exceed a given threshold.

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