Answer
(a.) 100.
(b.) 106.
(c.) 158.
Work Step by Step
The given function is
$C=N(\frac{6}{5})^t$
Where $C$ is the number of cells in the culture.
(a.) The given values are
Time $t=2\; hours$
Number of cells $C=144$.
Substitute all values into the function.
$\Rightarrow 144=N(\frac{6}{5})^2$
Simplify.
$\Rightarrow 144=N(\frac{36}{25})$
$\Rightarrow 144\cdot \frac{25}{36}=N$
$\Rightarrow 100=N$
(b.) The given values are
Time $t=20\;minutes=\frac{20}{60}\; hours=\frac{1}{3}\;hours$
Substitute all values into the function.
$C=100(\frac{6}{5})^{\frac{1}{3}}$
Simplify.
$C=106$ (approx).
(c.) The given values are
Time $t=2.5\;hours$
Substitute all values into the function.
$C=100(\frac{6}{5})^{2.5}$
Simplify.
$C=158$ (approx).
