MATH SOLVE

3 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)x. Rewrite the function to show how quickly the weeds grow each day. A.f(x) = 86(1.04)x; grows approximately at a rate of 0.4% daily B.f(x) = 86(1.04)7x; grows approximately at a rate of 4% daily C.f(x) = 86(1.29)7x; grows approximately at a rate of 20% daily D.f(x) = 86(1.297)x; grows approximately at a rate of 2% daily

Accepted Solution

A:

The exponential function which shows the daily growth rate of the weed is [tex] f(x) = 86( {1.04 )}^{7x} [/tex] The growth function for the growth rate per week is given as : [tex]f(x) = 86( {1.29)}^{x} [/tex]An exponential function is generally written thus :[tex] f(x) = ( {1 + r )}^{x} [/tex] The growth rate per week, r = 29% = 0.29The growth rate per day can be calculated thus : Number of days in a week = 7 Growth rate per day = 0.29 / 7 = 0.0414 = 0.04Rewriting the function :[tex] f(x) = 86( {1 + 0.0414 )}^{7x} [/tex] [tex] f(x) = 86( {1.04 )}^{7x} [/tex] Hence, 4% represents the daily growth rate of the weed.Learn more :