Question

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.

Answer 1

Answer:

$56\%$

Step-by-step explanation:

The function is

$y=a(1230.25)^{t/16}$

We need to convert it into the form

$y=a(1+r)^n$

where r = Growth rate

n = Time taken

a = Initial quantity

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

1.56 can be written as $1+0.56$, so

$y=(1+0.56)^t$

So, $r=0.56$

In percent $0.56\times 100\%=56\%$

The duckweed will increase each day by $56\%$.