Answer
The rate at which a substance grows is given by
$$
R^{\prime}(x)=150 e^{0.2x}
$$
where $x$ is the time (in days). The total accumulated growth during the first 3.5 days is given by:
$$
\begin{aligned} \int_{0}^{3.5} R^{\prime}(x) d x &=\int_{0}^{3.5} 150 e^{0.2 x} d x \\ & \approx 760.3 \end{aligned}
$$
Work Step by Step
The rate at which a substance grows is given by
$$
R^{\prime}(x)=150 e^{0.2x}
$$
where $x$ is the time (in days). The total accumulated growth during the first 3.5 days is given by:
$$
\begin{aligned} \int_{0}^{3.5} R^{\prime}(x) d x &=\int_{0}^{3.5} 150 e^{0.2 x} d x \\ &=\left.150 \cdot \frac{e^{0.2 x}}{0.2}\right|_{0} ^{3.5} \\ &=\left.750 e^{0.2 x}\right|_{0} ^{3.5} \\ &=750 e^{0.7}-750 e^{0} \\ & \approx 760.3 \end{aligned}
$$
