Question

part 1 of 3
a blogger found that the number of visits to her website increases 5.6% annually. the website has 80,000 visits this year. write an exponential model to represent this situation. by what percent does the number of visits increase daily? explain how you found the daily rate.

the exponential model that represents the situation is $y = $
(use integers or decimals for any numbers in the expression. type an expression using $t$ as the variable.)

Explanation:

Step1: Define annual growth formula

$y = a(1 + r)^t$, where $a=60000$, $r=0.056$

Step2: Adjust for daily time scale

Replace $t$ with $\frac{t}{365}$ to model daily time:
$y = 60000(1.056)^{\frac{t}{365}}$

Step3: Calculate daily growth factor

Let daily factor = $b$, so $b^{365}=1.056$. Solve for $b$:
$b = 1.056^{\frac{1}{365}} \approx 1.00015$

Step4: Find daily percentage rate

Daily rate = $(b - 1) \times 100\% \approx (1.00015 - 1) \times 100\% = 0.015\%$

Answer:

$y = 60000(1.056)^{\frac{t}{365}}$
Daily increase rate: ~0.015%