Chapter 7 - Section 7.2 - Exponential Change and Separable Differential Equations - Exercises - Page 410: 29

$2.8 \times 10^{14}$

Given: $y=2$ and $t=0.5$; $y_0=1$ The exponential growth can be written as: $y=y_0e^{kt}$ Now, when t = 1 hour Then $2=e^{0.5k}$ or, $\ln 2=0.5 k \implies k=\dfrac{\ln 2}{0.5}=\ln 4$ Now, at the end of the $24$ hrs, we have Hence, $y =e^{24 \ln 4} =4^{24} $ or, $y= 2.8 \times 10^{14}$