Question

The equation y equals 5 times 3 to the power of 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 10,000?

Answer 1

To find out how many weeks it will take for the number of infected people to reach 10,000, you can set up the equation:

y = 5 * 3^t

Here, y represents the number of infected people, and t represents time in weeks.

You want to find t when y = 10,000. So, the equation becomes:

10,000 = 5 * 3^t

Now, you need to solve for t:

First, divide both sides by 5:

10,000 / 5 = 3^t

2,000 = 3^t

Now, you need to find the value of t. Since 3^t is 2,000, you can express this in terms of a logarithm:

t = log₃(2,000)

Using a calculator or a computer math tool, you can find the approximate value of t:

t ≈ 6.91 weeks

So, it will take approximately 6.91 weeks for the number of infected people to reach 10,000 during the measles outbreak. Rounded up, this means it will take 7 weeks.