MATH SOLVE

4 months ago

Q:
# Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents the weekly weed growth: f(x) = 86(1.29). Rewrite the function to show how quickly the weeds grow each day.A.f(x) = 86(1.04)*; grows approximately at a rate of 0.4% dailyB.f(x) = 86(1.04)7%, grows approximately at a rate of 4% dailyC.f(x) = 86(1.29)7%; grows approximately at a rate of 20% dailyD.f(x) = 86(1.297); grows approximately at a rate of 2% daily

Accepted Solution

A:

Answer:Option A. [tex]f(x)=86[1.04]^{x}[/tex] ; grows approximately at a rate of 0.4% dailyStep-by-step explanation:we have[tex]f(x)=86(1.29)^{x}[/tex]wheref(x) the number of weeds in the gardenx ----> the number of weeksCalculate how quickly the weeds grow each dayRemember that a week is equal to seven daysso[tex]f(x)=86(1.29)^{\frac{x}{7}}[/tex]Using the law of exponents b^(x/a) = b^(x*(1/a)) = (b^(1/a))^xso[tex]f(x)=86[(1.29)^{\frac{1}{7}}]^{x}[/tex][tex]f(x)=86[1.04]^{x}[/tex]thereforeThe rate is approximately 1.04=1+rr=1.04-1=0.04=4% daily