the population of a city of 750,000 us devastated by an unknown virus that kills 20% of the population per day. The use the equation to find: how many people are left after a week. write the exponential equation to solve and use what each variable represents.

To solve this problem, we can use the exponential decay formula, which models the situation where a value decreases over time. The formula for exponential decay is:

N(t) = N0 * e^(-kt)

Where:
- N(t) represents the number of people at time t
- N0 represents the initial population size
- e is the base of the natural logarithm (approximately 2.71828)
- k is the decay constant (which represents the rate at which the population decreases over time)
- t represents time (in this case, measured in days)

In this scenario:
- N0 (initial population size) is 750,000
- t is 7 days (a week)
- The virus kills 20% of the population per day, meaning the decay constant k = 0.20

With this information, we can substitute these values into the exponential decay formula and calculate the number of people left after a week:

N(t) = 750,000 * e^(-0.20t)

N(t) = 750,000 * e^(-0.20*7)

N(t) = 750,000 * e^(-1.40)

Using a calculator, you can evaluate e^(-1.40) and then multiply it by 750,000 to find the number of people left after a week.