$6\mathrm{.}2$

Find the function $y=f(t)$ passing through the point $(0,18)$ with the given differential equation. Use a graphing utility to graph the solution.

$y=,\frac{dy}{dt}=\frac{8}{9}y$

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$6.[0/1$ Points$]$

LARCALC$126\mathrm{.}2\mathrm{.}026.$MI$.$

Write and find the general solution of the differential equation that models the verbal statement. $($Use $k$ for the constant of proportionality.$)$

The rate of change of $P$ is proportional to $P.$

$\frac{dP}{dt}=$

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$P(t)=$

$$ Check that you have the right number of constants. Note the letter e will be treated as Euler's number $2\mathrm{.}718....$

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

When $t=0,P=6,000$ and when $t=1,P=5,700.$ What is the value of $P$ when $t=4?$

$P(4)=$

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