Calculus Examples

$P (t) = 9.906 {(0.997)}^{t}$

Step 1

Since $9.906$ is constant with respect to $t$ , the derivative of $9.906 \cdot {0.997}^{t}$ with respect to $t$ is $9.906 \frac{d}{d t} [{0.997}^{t}]$ .

$9.906 \frac{d}{d t} [{0.997}^{t}]$

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d t} [a^{t}]$ is $a^{t} \ln (a)$ where $a$ = $0.997$ .

$9.906 ({0.997}^{t} \ln (0.997))$

Step 3

Multiply $\ln (0.997)$ by $9.906$ .

$- 0.02976266 \cdot {0.997}^{t}$