The spread of a fungal infection in an ant colony can be modeled by dt dy y+1 %3D where t is the time in hours 2/7 and y is the percent of the ants infected. At t = 1 only three percent of the ants are infected. a) Write an equation for the line tangent to the graph of y at t = 1. Use the tangent line to approximate the percentage of the colony infected at t = 1.2. b) Find y explicitly in terms of t.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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A graphing calculator may be used for the following problem.
The spread of a fungal infection in an ant colony can be modeled by
dy y+1
dt
where t is the time in hours
and y is the percent of the ants infected. Att = 1 only three percent of the ants are infected.
a) Write an equation for the line tangent to the graph of y at t = 1. Use the tangent line to
approximate the percentage of the colony infected at t = 1.2.
b) Find y explicitly in terms of t.
Transcribed Image Text:A graphing calculator may be used for the following problem. The spread of a fungal infection in an ant colony can be modeled by dy y+1 dt where t is the time in hours and y is the percent of the ants infected. Att = 1 only three percent of the ants are infected. a) Write an equation for the line tangent to the graph of y at t = 1. Use the tangent line to approximate the percentage of the colony infected at t = 1.2. b) Find y explicitly in terms of t.
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