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 \( y=5\left(2^{t}\right) \) 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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