a marketing specialist determines that when a certain product is released, the number of social media…

a marketing specialist determines that when a certain product is released, the number of social media references to it can be modeled by $f(t)=600 + 3log_{2}(t)$ where $t$ is the number of days since the release. determine $f(t)=$ $f(13)=$

a marketing specialist determines that when a certain product is released, the number of social media references to it can be modeled by $f(t)=600 + 3log_{2}(t)$ where $t$ is the number of days since the release. determine $f(t)=$ $f(13)=$

Answer

Explanation:

Step1: Recall derivative rules

The derivative of a constant is 0, and the derivative of $\log_a(u)$ is $\frac{1}{u\ln(a)}\cdot u'$. For $f(t)=600 + 3\log_2(t)$, the derivative of 600 is 0, and for $y = \log_2(t)$, using the formula $\frac{d}{dt}\log_a(t)=\frac{1}{t\ln(a)}$, the derivative of $3\log_2(t)$ is $3\times\frac{1}{t\ln(2)}$.

Step2: Find $f'(t)$

$f'(t)=\frac{3}{t\ln(2)}$

Step3: Calculate $f'(13)$

Substitute $t = 13$ into $f'(t)$. So $f'(13)=\frac{3}{13\ln(2)}$

Answer:

$f'(t)=\frac{3}{t\ln(2)}$ $f'(13)=\frac{3}{13\ln(2)}$