Answer
$t(n)=7.5$ $then$ $n≈1.386$
$t(n)=1.8$ $then$ $n≈-2.599$
Work Step by Step
Solving the equation $t(n)=y$, then we have:
$t(n)=y ⇔ \frac{15}{1+2e^{-0.5n}}=y ⇔ \frac{1+2e^{-0.5n}}{15}=\frac{1}{y}⇔$
$⇔1+2e^{-0.5n}=\frac{15}{y}⇔2e^{-0.5n}=\frac{15}{y}-1⇔$
$⇔e^{-0.5n}=(\frac{15}{y}-1):2⇔-0.5n=\ln((\frac{15}{y}-1):2)⇔$
$⇔n=\frac{\ln((\frac{15}{y}-1):2)}{(-0.5)}$
For $y=7.5$ $then$ $n=1.386$ and for $y=1.8$ $then$ $n=-2.599$
