The equation \( y=2\left(3^{\dagger}\right) \) shows the number of infected people from an outbreak of the Norovirus. The variable \( y \) represents the number of infected people, and trepresents time in weeks. In how many weeks will the number of infected people reach 1,458 ? a.) 10 weeks b.) 5 weeks c.) 12 weeks d.) 6 weeks

To find out in how many weeks the number of infected people will reach 1,458, we can set up the equation: \[ 1458 = 2(3^t) \] First, divide both sides by 2: \[ 729 = 3^t \] Next, since \( 729 \) is equal to \( 3^6 \) (as \( 3^6 = 729 \)), we can conclude: \[ t = 6 \] Therefore, the correct answer is **d.) 6 weeks**. Now, let’s delve into some interesting aspects! The Norovirus, often known as the "winter vomiting bug," has a fascinating history. It was first identified in an outbreak in Norwalk, Ohio, in 1968. It's quite an enigma—it spreads rapidly, making it a major public health challenge, especially in crowded places like cruise ships and schools! For real-world application, understanding the dynamics of infections like Norovirus can help in planning strategies for containment. By modeling the spread of infections using equations similar to yours, public health officials can predict outbreaks and allocate resources more effectively, ensuring timely interventions to protect communities.