MATHEMATICS HIGH SCHOOL

The function f(x) = 4(3)x represents the growth of a dragonfly population every year in a remote swamp. Erin wants to manipulate the formula to an equivalent form that calculates four times a year, not just once a year. Which function is correct for Erin's purpose, and what is the new growth rate?

Answers

Answer 1

Answer:

Answer:

$f(x) = 4(1.32)^x$ function is correct for Erin's purpose and the new growth rate is 32%

Step-by-step explanation:

Growth rate function: $a(1+r)^x$ --A

where r is the rate of growth

We are given that The function $f(x) = 4(3)^x$ represents the growth of a dragonfly population every year in a remote swamp.

Now Erin wants to manipulate the formula to an equivalent form that calculates four times a year, not just once a year

So, equation becomes: $f(x) = 4(3^(1)/(4))^x$

$f(x) = 4(1.32)^x$

Now on comparing with A

1.32=1+r

0.32=r

So, New growth rate = 0.32=32%

Hence $f(x) = 4(1.32)^x$ function is correct for Erin's purpose and the new growth rate is 32%

Answer 2

Answer: There are 12 months a year, and if the growth is to be calculated four times a year, the interval would be every three months.

We use the variable
z as the number of 3 months per year

So,
x = z/4

Substituting, the new growth rate would be:
f(z) = 4(3)^(z/4)

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Answers

Answer:

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Step-by-step explanation:

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Answers

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