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The spread of a fungal infection in an ant colony can be modeled by 2 where t is the time in hours 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.

The spread of a fungal infection in an ant colony can be modeled by 2 where t is the time in hours 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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FRQ 1 A graphing calculator may be used for the following problem. The spread of a fungal infection in an ant colony can be modeled by = where t is the time in hours 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.
Transcribed Image Text:FRQ 1 A graphing calculator may be used for the following problem. The spread of a fungal infection in an ant colony can be modeled by = where t is the time in hours 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.
FRQ 2 A graphing calculator may NOT be used for the following problem. Consider the differential equation = x(y – 1). a) On the axes provided, sketch a slope field for the given differential equation at the 8 given points. b) Let y = f(x) be the particular solution to the given differential equation with the initial condition A1) = 2. Write an equation for the line tangent to the graph of y = f{x) at x = 1. Use your equation to approximate f(1.5). c) Find the particular solution y = flx) to the given differential equation with the initial condition A(1) = 2.
Transcribed Image Text:FRQ 2 A graphing calculator may NOT be used for the following problem. Consider the differential equation = x(y – 1). a) On the axes provided, sketch a slope field for the given differential equation at the 8 given points. b) Let y = f(x) be the particular solution to the given differential equation with the initial condition A1) = 2. Write an equation for the line tangent to the graph of y = f{x) at x = 1. Use your equation to approximate f(1.5). c) Find the particular solution y = flx) to the given differential equation with the initial condition A(1) = 2.
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