Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 18% each week. The following function represents the weekly weed growth: f(x) = 86(1.18)x. Rewrite the function to show how quickly the weeds grow each day.

f(x) = 86(1.02)x; grows approximately at a rate of 0.2% daily
f(x) = 86(1.18)7x; grows approximately at a rate of 1.8% daily
f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily
f(x) = 86(1.187)x; grows approximately at a rate of 0.18% daily

Question

Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 18% each week. The following function represents the weekly weed growth: f(x) = 86(1.18)x. Rewrite the function to show how quickly the weeds grow each day.

f(x) = 86(1.02)x; grows approximately at a rate of 0.2% daily
 f(x) = 86(1.18)7x; grows approximately at a rate of 1.8% daily
 f(x) = 86(1.02)7x; grows approximately at a rate of 2% daily
 f(x) = 86(1.187)x; grows approximately at a rate of 0.18% daily

Vocaloid · Answer

the weekly growth rate is 18% or 0.18

Divide this by 7 to get the daily growth rate r. then calculate 1 + r. this is the new base of the new equation.

Now, for the exponent, instead of x, it has to be 7x now. x still represents the weekly growth rate, so if we use the daily growth rate as the base, we have to use 7 days * x as the new exponent.