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

`56\%`

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* 100\%=56\%`

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