Question

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?

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%

Answer 1

I think you mean f(x)=4(4)^x, not f(x)=4(4)x. Small but important difference!

Answer 2

\[y=4(4)^{x}\]

Answer 3

The " ^ " symbol signifies exponentiation.

Answer 4

yes

Answer 5

@mathmale

Answer 6

hello @SolomonZelman

Answer 7

Hello

Answer 8

where ya at @mathmale

Answer 9

i need yo help @phi

Answer 10

@phi @phi @phi @phi @phi @phi @phi @phi

Answer 11

For example, the following problem:

The function \(\large\color{#003366}{\displaystyle f(x)=2(10)^x }\) represents the growth
of a fly population every year in a remote swamp. John
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 John's purpose, and what
is the new growth rate?

\(\large\color{#003366}{\displaystyle f(x)_{\rm ~[once ~a ~ year]}=2(10)^x }\)

\(\large\color{#003366}{\displaystyle f(x)_{\rm ~[4~times ~a ~ year]}=2(\sqrt[4]{10})^{4x} }\)

Now, each x is 4 times a year, and the 4th root
is there to keep the function equivalent.

Approximately,

\(\large\color{#003366}{\displaystyle f(x)_{\rm ~[4~times ~a ~ year]}=2(1.78)^{4x} }\)

Now, the percent rate!

You are growing, times 1.78 every time.
That is equivalent to saying that each time is 178% of the previous,
or in other words, you are growing by 78%.

Answer 12

I meant that eadh x is 1/4th of a year...

Answer 13

Nice work, Solomon! Stress that this was an EXAMPLE that your student needs to apply to his or her original problem statement.

Answer 14

Thank you!