Question

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?

Answer 1

you probably meant \(\normalsize\color{royalblue}{ \rm f(x)=4(3)^x }\)

Answer 2

yea

Answer 3

where
f(0) is the initial population.
f(1) is the population after year 1.
f(2) is the population after year 2.

Now, Erin wants a formula that will be calculating the growth every quarter of the year.

Answer 4

I will give you an example of what I would do if I wanted to manipulate our formula so that it will be giving the growth every half of a year.

\(\normalsize\color{royalblue}{ \rm f(x)=4(3)^{x/2} }\)

and now,
f(0) => initial population
f(1) => population after 1/2 of a year
f(2) => population after 2/2 of a year (or 1 year)
f(3) => population after 3/2 of a year (or 1 year and a half)
f(4) => population after 4/2 of a year (or 2 years)
f(5) => population after 5/2 of a year (or 2 years and a half)
f(4) => population after 6/2 of a year (or 3 years)

Answer 5

whaat? im so confused :c

Answer 6

do you have something specific to ask, or you just don't get anything from what I posted (not that I am claiming to be anything like a very good tutor)

Answer 7

how does half a year have to do with her wanting to know 4 times a year?

Answer 8

I gave you example how to do a formula that tells you a growth after 1/2 of a year.

Answer 9

just an example, not answer....

Answer 10

these are my options f(x) = 4(3)x; growth rate 300% f(x) = 4(3)x, growth rate 4% f(x) = 4(1.32)x; growth rate 4% f(x) = 4(1.32)4x; growth rate 32%

Answer 11

ok

Answer 12

I would like to see your attempt to generate the requested formula please/

Answer 13

so she wants 4*(1.32)^x?

Answer 14

yes

Answer 15

\(\normalsize\color{royalblue}{ \rm f(x)=4(3)^x }\)
\(\normalsize\color{royalblue}{ \rm f(x)=4(3)^{x/4} }\)
\(\normalsize\color{royalblue}{ \rm f(x)=4(\sqrt[4]{3})^{x} }\)
\(\normalsize\color{black}{ \rm \sqrt[4]{3}\approx 1.32 }\)
\(\normalsize\color{royalblue}{ \rm f(x)=4(1.32)^{x} }\) (answer)

Answer 16

so the growth rate is 32 %?

Answer 17

yes

Answer 18

because you are taking 132% of the entire previous amount when multiplying times 1.32.

That means you are adding another 32% to the 100% you had already.

Answer 19

so f(x) 3(1.32)^4x with a growth rate of 32?

Answer 20

f(x)=...
correct

Answer 21

would you mind helping me with another one ??

Answer 22

I am with another student right now, but when I finish and if I have more time, I will attempt my best to help you.