Question

Write and solve the differential equation that models the verbal statement. (Use k for the constant of proportionality.) The rate of change of y is proportional to y. When $x = 0$, $y = 14$, and when $x = 5$, $y = 49$. What is the value of y when $x = 10$? $\frac{dy}{dx} = 14k^x$ $y = \frac{1}{2}ln(\frac{49}{14})^{\frac{x}{5}}$ Your answer cannot be understood or graded. More Information Evaluate the solution at the specified value of the independent variable. $y = 343$

          Write and solve the differential equation that models the verbal statement. (Use k for the constant of proportionality.)
The rate of change of y is proportional to y. When $x = 0$, $y = 14$, and when $x = 5$, $y = 49$. What is the value of y when $x = 10$?
$\frac{dy}{dx} = 14k^x$
$y = \frac{1}{2}ln(\frac{49}{14})^{\frac{x}{5}}$
Your answer cannot be understood or graded. More Information
Evaluate the solution at the specified value of the independent variable.
$y = 343$

Write and solve the differential equation that models the verbal statement. (Use k for the constant of proportionality.)
The rate of change of y is proportional to y. When x = 0, y = 14, and when x = 5, y = 49. What is the value of y when x = 10?
(dy)/(dx) = 14k^x
y = (1)/(2)ln((49)/(14))^(x)/(5)
Your answer cannot be understood or graded. More Information
Evaluate the solution at the specified value of the independent variable.
y = 343

Added by Terry H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Keerti J

03/03/2022

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Step 1: Write the differential equation: dy/dx = k y. Show more…

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Write and solve the differential equation that models the verbal statement. (Use k for the constant of proportionality.) The rate of change of y is proportional to y. When x = 0, y = 14, and when x = 5, y = 49. What is the value of y when x = 10? dy/dx = ky, y = ? Evaluate the solution at the specified value of the independent variable. y = [0/3 Points] DETAILS PREVIOUS ANSWERS LARCALCPRECALC38.4.021. Write and solve the differential equation that models the verbal statement. (Use k for the constant of proportionality.) The rate of change of y is proportional to y. When x = 0, y = 14, and when x = 5, y = 49. What is the value of y when x = 10? 14k = 14 49 = 14k * 5 k = 49 / 70 k = 7 / 10 y = 14 * e^(7/10 * 10) y = 14 * e^7 y = 14 * 1096.633 y = 15392.262 Evaluate the solution at the specified value of the independent variable 343 X