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 $x = 10$?
$\frac{dy}{dx} = 14k^x$
$y = \frac{1}{2}ln(\frac{49}{14})^{\frac{x}{5}}$
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Evaluate the solution at the specified value of the independent variable.
$y = 343$
