please help!!!! for medal!! The function f(x) = 16(2)x represents the growth of a bee population every year in a remote swamp. Jennifer wants to manipulate the formula to an equivalent form that calculates two times a year, not just once a year. Which function is correct for Jennifer's purpose, and what is the new growth rate?

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please help!!!! for medal!! The function f(x) = 16(2)x represents the growth of a bee population every year in a remote swamp. Jennifer wants to manipulate the formula to an equivalent form that calculates two times a year, not just once a year. Which function is correct for Jennifer's purpose, and what is the new growth rate?

Mathematics
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@phi i have no idea what to do
  • phi
maybe we write it as \[ f(x)= 16\cdot 2^x = 16 \cdot (1+1)^x \] and to change to every 6 months \[ f(x)= 16\cdot (1+1/2)^{2x}= 16 \cdot 1.5^{2x} \] but I am guessing
f(x) = 16(2)x; growth rate 200% f(x) = 16(2)2x; growth rate 8% f(x) = 16(1.41)x; growth rate 8% f(x) = 16(1.41)2x; growth rate 41% these are the choices

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if this helps you @phi
  • phi
I would go with choice D
okayy agian thank you so much !
  • phi
I guess the idea is to write the exponent as 2x (twice as many as before) but to not change things we do this \[ \left(2\right)^{\frac{1}{2} \cdot 2x } \] and then interpret that as \[ \left(2^{\frac{1}{2} }\right)^{2x} \] and 2^(1/2) is sqr(2) = 1.41, so \[ (1.41)^{2x} \] and we put the 16 in there for the final answer \[ 16(1.41)^{2x} \]
thank you!

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