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Blizzard [7]
3 years ago
12

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp. Jackie wants to manipulate the

formula to an equivalent form that calculates three times a year, not just once a year. Which function is correct for Jackie's purpose, and what is the new growth rate?
Answer Options:

f(x) = 4(4)^x; growth rate 400%

f(x) = 4(4)^3x; growth rate 4%

f(x) = 4(1.59)^3x; growth rate 59%

f(x) = 4(1.59)^x; growth rate 4%
Mathematics
1 answer:
Sauron [17]3 years ago
5 0

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp.

calculates three times a year, not just once a year.

f(x)= 4(4)^x

3 times a year

so x becomes 3x

f(x)= 4(1+r)^{3x}

4(4)^x=4(1+r)^{3x}

Take log on both sides

log(4)^x=log(1+r)^{3x}

log(4)^x=log(1+r)^{3x}

Use log property and move exponent before log

xlog(4)=3xlog(1+r)}

Divide both sides by x

log 4 = 3 log(1+r)

Solve for '1+r'

log 4 = log(1+r)^3

Remove log from both sides

4 = (1+r)^3

take cube root on both sides

1.584740= 1+r

1+r = 1.59

f(x)= 4(1+r)^{3x}

so equation becomes

f(x)= 4(1.59)^{3x}

1+r = 1.59

subtract 1 from both sides

So r= 59 = 59%

So growth factor is 59%

Answer is option C



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