Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents the weekly weed growth: f(x) = 86(1.08)x. Rewrite the function to show how quickly the weeds grow each day.
f(x) = 86(1.08)7x; grows approximately at a rate of 5.6% daily
f(x) = 86(1.087)x; grows approximately at a rate of 0.56% daily
f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily
f(x) = 86(1.01)7x; grows approximately at a rate of 1% daily
Which one is it?
The correct answer is:
f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily
To rewrite the function to show how quickly the weeds grow each day, we need to convert the weekly growth rate to a daily growth rate.
The given function is f(x) = 86(1.08)^x, where x represents the number of weeks.
To convert the growth rate to daily, we divide the weekly growth rate by 7, since there are 7 days in a week.
Therefore, the daily growth rate can be represented by the function f(x) = 86(1.08/7)^x.
Simplifying further, f(x) = 86(1.08/7)^x = 86(0.154)^x.
Now, let's evaluate the function to determine the daily growth rate:
f(1) = 86(0.154)^1 ≈ 13.284
Since the initial number of weeds was 86, and after one day there would be approximately 13.284 weeds, the daily growth rate is calculated by dividing the number of new weeds (13.284) by the initial number of weeds (86), and then multiplying by 100 to express it as a percentage:
Daily growth rate ≈ (13.284/86) * 100 ≈ 15.426%.
Therefore, the correct answer is: f(x) = 86(0.154)^x; grows approximately at a rate of 15.426% daily.
multiply by 1.08 every week
but we are doing per day
1.08 = x^7
7 log x = log 1.08
log x = 0.004775
x = 1.011
so
1.1 percent daily