Question

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

Answer 1

The exponential function which shows the daily growth rate of the weed is $f(x) = 86( {1.04 )}^{7x}$

The growth function for the growth rate per week is given as :

• $f(x) = 86( {1.29)}^{x}$

An exponential function is generally written thus :

• $f(x) = ( {1 + r )}^{x}$

The growth rate per week, r = 29% = 0.29

The growth rate per day can be calculated thus :

• Number of days in a week = 7

• Growth rate per day = 0.29 / 7 = 0.0414 = 0.04

Rewriting the function :

• $f(x) = 86( {1 + 0.0414 )}^{7x}$

• $f(x) = 86( {1.04 )}^{7x}$

Hence, 4% represents the daily growth rate of the weed.

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