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Math·Advanced Math·Nonlinear functions

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At different times on a certain day, a manager at a theme park recorded the number of visitors. An exponential model gives the estimated number of visitors, $V$, at the theme park $t$ hours after the theme park opened, where $t\le 3$. Based on the model, $80$ visitors were estimated to be at the theme park when it opened, and every $30$ minutes the estimated number of visitors increased by $150\%$ of the estimated number of visitors $30$ minutes earlier. Which of the following equations best represents this model?

A

$V=80(2.50{)}^{2t}$

B

$V=80(2.50{)}^{\frac{t}{30}}$

C

$V=80(1.50{)}^{2t}$

D

$V=80(1.50{)}^{\frac{t}{30}}$