Questions: The equation y=25(2^t) shows the number of infected people from an outbreak of E.coli. The variable y represents the number of infected people, and t represents time in weeks. In how many weeks will the number of infected people reach 800? a.) 6 weeks b.) 5 weeks c.) 3 weeks d.) 4 weeks

The equation y=25(2^t) shows the number of infected people from an outbreak of E.coli. The variable y represents the number of infected people, and t represents time in weeks.

In how many weeks will the number of infected people reach 800?
a.) 6 weeks
b.) 5 weeks
c.) 3 weeks
d.) 4 weeks

Transcript text: 16:31 Question Tutorials The equation $y=25\left(2^{t}\right)$ shows the number of infected people from an outbreak of E.coli. The variable $y$ represents the number of infected people, and $t$ represents time in weeks. In how many weeks will the number of infected people reach 800 ? a.) 6 weeks b.) 5 weeks c.) 3 weeks d.) 4 weeks SUBMIT MY ANSWER app.sophia.org

Solution

Solution Steps

Step 1: Set up the equation

Given the equation $ y = 25 \left(2^{t}\right) $, we need to find the value of $ t $ when $ y = 800 $. Substitute $ y = 800 $ into the equation: \[ 800 = 25 \left(2^{t}\right) \]

Step 2: Solve for $ 2^{t} $

Divide both sides of the equation by 25 to isolate $ 2^{t} $: \[ \frac{800}{25} = 2^{t} \] \[ 32 = 2^{t} \]

Step 3: Solve for $ t $

Recognize that $ 32 $ is a power of 2: \[ 32 = 2^{5} \] Thus, $ t = 5 $.

The number of infected people will reach 800 in 5 weeks.