1). Write and find the general solution of the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable. The rate of change of P is proportional to P. When t = 0, P = 6,000 and when t = 1, P = 3,900. What is the value of P when t = 4? Write the differential equation. (Use k for the constant of proportionality.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1). Write and find the general solution of the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable.

The rate of change of P is proportional to P. When t = 0, P = 6,000 and when t = 1, P = 3,900. What is the value of P when t = 4?

Write the differential equation. (Use k for the constant of proportionality.)

2). When an object is removed from a furnace and placed in an environment with a constant temperature of 80°F, its core temperature is 1500°F. One hour after it is removed, the core temperature is 1180°F.

(a)
Write an equation for the core temperature y of the object t hours after it is removed from the furnace. (Round your coefficients to four decimal places.)
y(t) = 
 
(b) Find the core temperature 8 hours after the object is removed from the furnace. (Round your answer to one decimal place.)
dP
dt
 = 
Solve the differential equation.
P = 

Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.)

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