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A biologist is studying the growth of a particular species of Algaze. She writes the following equation to show the radius of the algae f(d) in mm after d days f(d) = 7(1.06)d

User Jsuggs
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Explanation:

you did not write the actual question. what do you need to calculate, to characterize, to ... ?

I can give you here an explanation of the equation/function (for which you made a writing mistake here) :

f(d) = 7(1.06)d (as you wrote it)

you know that this is in long form

f(d) = 7 × 1.06 × d

all three terms are multiplied with each other.

correctly this would be

correctly this would bef(d) = 7(1.06)^d

correctly this would bef(d) = 7(1.06)^dor in long form

correctly this would bef(d) = 7(1.06)^dor in long formf(d) = 7 × (1.06)^d

anyway, the various terms of the function definition mean :

7 ... this is the starting size (7 mm) of the radius of the algea population.

7 ... this is the starting size (7 mm) of the radius of the algea population. 1.06 ... every day the radius increases by 6% (what was on the day before as 100% plus additional 6% is a 1 + 0.06 = 1.06 factor).

7 ... this is the starting size (7 mm) of the radius of the algea population. 1.06 ... every day the radius increases by 6% (what was on the day before as 100% plus additional 6% is a 1 + 0.06 = 1.06 factor).d ... is the number of days since the begin of the experiment

now to the mistake - the function should be

f(d) = 7(1.06)^d

the reason is in the explanation of 1.06. if d is not used as an exponent, the whole point of showing a 6% growth rate is lost.

f(d) = 7(1.06)d

would simply be

f(d) = 7.42d

that would mean the growth of the radius is an arithmetic sequence (adding the same constant every day, when the circle is still very small and then also the same when it gets large).

but in the matter of growth typically the growth rate is constant, but not the absolute growth.

it is therefore a geometric sequence (MULTIPLY every day by a constant factor).

so, the radius size after e.g. 4 days is NOT :

7.42 + 7.42 + 7.42 + 7.42 = 29.68 mm

remember, a multiplication is repeating the same addition multiple times.

it is also NOT

7 + 1.06 + 1.06 + 1.06 + 1.06 = 11.24 mm

for f(d) = 7 + (1.06)d

the radius size after e.g. 4 days really is

the radius size after e.g. 4 days really is7 × 1.06 × 1.06 × 1.06 × 1.06 = 8.83733872 mm

every day there is a 6% increment compared to the size of the previous day.

remember, an exponent is repeating the same multiplication multiple times.

User Smerlung
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