The number y of duckweed fronds in a pond after t days is y=a(1230.25)t/16, where a is the initial number of fronds. By what percent does the duckweed increase each day? Round your answer to the nearest whole number.

Respuesta :

Answer:

[tex]56\%[/tex]

Step-by-step explanation:

The function is

[tex]y=a(1230.25)^{t/16}[/tex]

We need to convert it into the form

[tex]y=a(1+r)^n[/tex]

where r = Growth rate

n = Time taken

a = Initial quantity

[tex]y=a(1230.25)^{t/16}\\\Rightarrow y=a((1230.25)^{1/16})^t\\\Rightarrow y=1.56^t[/tex]

1.56 can be written as [tex]1+0.56[/tex], so

[tex]y=(1+0.56)^t[/tex]

So, [tex]r=0.56[/tex]

In percent [tex]0.56\times 100\%=56\%[/tex]

The duckweed will increase each day by [tex]56\%[/tex].