Question

question 25

the equation \\(y = 15 \cdot 2^t\\) shows the number of infected people from an outbreak of the measles. 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 1200?

• 6.32 weeks
• 4.89 weeks
• 4.23 weeks
• 6.67 weeks

Explanation:

Set up the exponential equation

Using the Exponential Equations knowledge point

$$
LATEXBLOCK0
$$

Isolate the exponential term

Using the Exponential Equations knowledge point

$$
LATEXBLOCK1
$$

Solve for t using logarithms

Using the Logarithmic Equations and Logarithm Properties knowledge points

$$
LATEXBLOCK2
$$

Calculate the numerical value

Using the Logarithmic Equations knowledge point

$$
LATEXBLOCK3
$$

Answer:

• (A) 6.32 weeks (Correct answer)
• (B) 4.89 weeks
• (C) 4.23 weeks
• (D) 6.67 weeks