Question

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?

Answer 1

@phi i have no idea what to do

Answer 2

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

Answer 3

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

Answer 4

if this helps you @phi

Answer 5

I would go with choice D

Answer 6

okayy agian thank you so much !

Answer 7

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
\[ 16(1.41)^{2x} \]

Answer 8

thank you!