The exponential function showing the relationship between y (the city's population) and t (the number of years since the start of the study) can be written as follows:

y = 300,000 * (1 + 5.8/100)^t

Here's the step-by-step breakdown:

1. Start with the initial population: 300,000. This is the value of y when t=0.

2. Each year, the population increases by 5.8%. This can be written as a decimal by dividing 5.8 by 100, which gives 0.058.

3. The expression (1 + 0.058) represents the growth factor each year. If the population were to stay the same, the growth factor would be 1. Since the population is growing, the growth factor is greater than 1.

4. The exponent t represents the number of years that have passed. Each year, the population is multiplied by the growth factor.

5. Therefore, the exponential function is y = 300,000 * (1 + 0.058)^t. This function shows how the population y changes with time t.

Question

The exponential function showing the relationship between y (the city's population) and t (the number of years since the start of the study) can be written as follows:

y = 300,000 * (1 + 5.8/100)^t

Here's the step-by-step breakdown:

1. Start with the initial population: 300,000. This is the value of y when t=0.

2. Each year, the population increases by 5.8%. This can be written as a decimal by dividing 5.8 by 100, which gives 0.058.

3. The expression (1 + 0.058) represents the growth factor each year. If the population were to stay the same, the growth factor would be 1. Since the population is growing, the growth factor is greater than 1.

4. The exponent t represents the number of years that have passed. Each year, the population is multiplied by the growth factor.

5. Therefore, the exponential function is y = 300,000 * (1 + 0.058)^t. This function shows how the population y changes with time t.

Knowee AI · Accepted Answer

The exponential function showing the relationship between y (the city's population) and t (the number of years since the start of the study) can be written as follows:

y = 300,000 * (1 + 5.8/100)^t

Here's the step-by-step breakdown:

1. Start with the initial population: 300,000. This is the value of y when t=0.

2. Each year, the population increases by 5.8%. This can be written as a decimal by dividing 5.8 by 100, which gives 0.058.

3. The expression (1 + 0.058) represents the growth factor each year. If the population were to stay the same, the growth factor would be 1. Since the population is growing, the growth factor is greater than 1.

4. The exponent t represents the number of years that have passed. Each year, the population is multiplied by the growth factor.

5. Therefore, the exponential function is y = 300,000 * (1 + 0.058)^t. This function shows how the population y changes with time t.

At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 5.8%.Let t be the number of years since start of the study. Let y be the city's population.Write an exponential function showing the relationship between y and t.

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