The equation $$ y=5\left(2^{t}\right) $$ shows the number of infected people from an outbreak of influenza. 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 1,280?

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To find the time $$ t $$ when the number of infected people $$ y $$ reaches 1,280, we start with the equation:

$$
y = 5(2^t)
$$

We set $$ y $$ to 1,280:

$$
1280 = 5(2^t)
$$

Next, we divide both sides by 5 to isolate $$ 2^t $$:

$$
\frac{1280}{5} = 2^t
$$

Calculating the left side:

$$
\frac{1280}{5} = 256
$$

So we have:

$$
2^t = 256
$$

Next, we express 256 as a power of 2. We know that:

$$
256 = 2^8
$$

Thus, we can set the exponents equal to each other:

$$
t = 8
$$

Therefore, the number of infected people will reach 1,280 in $$ \boxed{8} $$ weeks.
The number of infected people will reach 1,280 in 8 weeks.

The equation shows the number of infected people from an
outbreak of influenza. The variable represents the number of infected
people, and represents time in weeks.
In how many weeks will the number of infected people reach 1,280?

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The equation shows the number of infected people from an outbreak of influenza. The variable represents the number of infected people, and represents time in weeks. In how many weeks will the number of infected people reach 1,280?