The growth rate of a colony of bacteria at temperature T^∘ F is P(T). The Fahrenheit temperature

Name: Problem 32, Chapter 8: Algebra Form and Function
Uploaded: 2022-04-12T03:14:56-08:00
Duration: 1 min 6 s
Channel: Nick Johnson
Description: The growth rate of a colony of bacteria at temperature T^∘ F is P(T). The Fahrenheit temperature T for H^∘ C is T=(9)/(5) ·H+32 Find an expression for Q(H), the growth rate as a function of H

step 1 Hello, so here we have the growth rate of a colony of bacteria at temperature T degrees Fahrenhe

Question

The growth rate of a colony of bacteria at temperature $T^{\circ} \mathrm{F}$ is $P(T)$. The Fahrenheit temperature $T$ for $H^{\circ} \mathrm{C}$ is $$ T=\frac{9}{5} \cdot H+32 $$ Find an expression for $Q(H),$ the growth rate as a function of $H$

   The growth rate of a colony of bacteria at temperature $T^{\circ} \mathrm{F}$ is $P(T)$. The Fahrenheit temperature $T$ for $H^{\circ} \mathrm{C}$ is
$$
T=\frac{9}{5} \cdot H+32
$$
Find an expression for $Q(H),$ the growth rate as a function of $H$

Algebra Form and Function

William G. McCallum,… 1st Edition

Chapter 8, Problem 32

Instant Answer

Solved by Expert Nick Johnson

04/12/2022

Step 1

We are also given the conversion formula from Celsius to Fahrenheit, which is $T=\frac{9}{5} \cdot H+32$. Show more…

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The growth rate of a colony of bacteria at temperature $T^{\circ} \mathrm{F}$ is $P(T)$. The Fahrenheit temperature $T$ for $H^{\circ} \mathrm{C}$ is $$ T=\frac{9}{5} \cdot H+32 $$ Find an expression for $Q(H),$ the growth rate as a function of $H$

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Key Concepts

Composite Functions

Composite functions refer to the process of applying one function to the results of another. In this context, the growth rate function P(T) is composed with the function that converts a temperature from Celsius to Fahrenheit. The new function, Q(H), is defined by substituting the Celsius-to-Fahrenheit conversion (T = (9/5)·H + 32) into P, yielding Q(H) = P((9/5)·H + 32).

Temperature Conversion

Temperature conversion is the process of converting a temperature value from one scale to another, such as from Celsius to Fahrenheit. This involves applying a linear transformation—in this case, multiplying the Celsius temperature H by 9/5 and then adding 32—to obtain the equivalent Fahrenheit temperature. Understanding this conversion is crucial when relating measurements or functions defined in one temperature scale to another.

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