A circular water stain on your home ceiling had a diameter of about 4 inches across on Monday at 8 A.M. On Tuesday at the same time it was about 5.3 inches across. The unit for time is days.

(1) Calculate the growth rate as a percentage to at least the nearest 10-thousandth over this time period.

(2) Assume that the growth rate can be applied over the next 5 days. Calculate the estimated diameter of the stain in 5 days from the initial measurement using discrete exponential growth. inches across

(3) Calculate the estimated diameter of the stain in 5 days from the initial measurement using a linear growth. inches across

To calculate the growth rate as a percentage over the given time period, you need to calculate the percentage increase in the diameter of the water stain.

(1) Growth rate as a percentage:

Step 1: Calculate the difference in diameter between Monday and Tuesday.
Difference = 5.3 inches - 4 inches = 1.3 inches

Step 2: Calculate the percentage increase.
Percentage_increase = (Difference / Initial diameter) * 100
Percentage_increase = (1.3 inches / 4 inches) * 100

Rounding the answer to the nearest 10-thousandth gives us:
Percentage_increase ≈ 32.5%

Therefore, the growth rate as a percentage to at least the nearest 10-thousandth over this time period is 32.5%.

(2) Estimated diameter using discrete exponential growth:

To estimate the diameter of the stain in 5 days using discrete exponential growth, we need to apply the growth rate calculated above.

Step 1: Calculate the daily growth rate.
Daily_growth_rate = Percentage_increase / 100
Daily_growth_rate = 32.5% / 100
Daily_growth_rate = 0.325

Step 2: Calculate the estimated diameter in 5 days.
Estimated_diameter = Initial diameter * (1 + Daily_growth_rate)^number_of_days
Estimated_diameter = 4 inches * (1 + 0.325)^5

Calculating the estimated diameter using a calculator gives us:
Estimated_diameter ≈ 6.815 inches

Therefore, the estimated diameter of the stain in 5 days from the initial measurement using discrete exponential growth is approximately 6.815 inches.

(3) Estimated diameter using linear growth:

To estimate the diameter of the stain in 5 days using linear growth, we assume that the growth is constant over time.

Step 1: Calculate the daily growth rate.
Daily_growth_rate = Difference / number_of_days
Daily_growth_rate = 1.3 inches / 1 day

Step 2: Calculate the estimated diameter in 5 days.
Estimated_diameter = Initial diameter + (Daily_growth_rate * number_of_days)
Estimated_diameter = 4 inches + (1.3 inches/day * 5 days)

Calculating the estimated diameter using a calculator gives us:
Estimated_diameter ≈ 10.5 inches

Therefore, the estimated diameter of the stain in 5 days from the initial measurement using linear growth is approximately 10.5 inches.