## anonymous one year ago 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?

1. anonymous

@phi i have no idea what to do

2. 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

3. anonymous

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

4. anonymous

if this helps you @phi

5. phi

I would go with choice D

6. anonymous

okayy agian thank you so much !

7. 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 $16(1.41)^{2x}$

8. anonymous

thank you!