Question

Initially, there were only 3 weeds at a park. The weeds grew at a rate of 5% each week. The following function represents the weekly weed growth: f(x) = 3(1.05)x. Rewrite the function to show how quickly the weeds grow each day and calculate this rate as a percentage.

Answer 1

The function can be rewritten to show daily growth by dividing x by 7. The daily growth rate can be calculated using the formula provided.

Step-by-step explanation:

The given function is f(x) = 3(1.05)^x, where x represents the number of weeks. To rewrite the function to show how quickly the weeds grow each day, we need to convert the growth rate from weekly to daily. Since there are 7 days in a week, the daily growth rate would be 1/7th of the weekly growth rate. Therefore, the function can be rewritten as:

f(x) = 3(1.05)^(x/7)

To calculate the daily growth rate as a percentage, we can use the formula:

Percentage Growth Rate = [(Daily Growth Rate - Initial Value) / Initial Value] * 100

Let's calculate the daily growth rate:

Daily Growth Rate = (1.05)^(1/7) - 1

Percentage Growth Rate = [(Daily Growth Rate - 1) / 1] * 100