Question

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.) $\frac{dP}{dt} = kP$ Solve the differential equation. $P = 6000e^{0.95t}$ Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.) 268207.107 

          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.)
$\frac{dP}{dt} = kP$
Solve the differential equation.
$P = 6000e^{0.95t}$
Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.)
268207.107
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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.) (dP)/(dt) = kP Solve the differential equation. P = 6000e^0.95t Evaluate the solution at the specified value of the independent variable. (Round your answer to three decimal places.) 268207.107

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The rate of change of P is proportional to p. When p = 6,000 and when t = 1, p = 300. What is the value of P when t = 47? Write the differential equation (Use A for the constant of proportionality). KP Solve the differential equation 60000.95 Evaluate the expression 268207107 X Submit. Answer
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Transcript

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00:01 In this question, we have to write the differential equation for the given statement.
00:12 Given rate of change of y with respect to x is proportional to y square.
00:56 D .y upon d x is proportional to y square...
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