Question

Someone plz help!!!

A population of rabbits at anytime t, measured in days, is represented by the function p(t)= 50(2)^t/80. How many days does it take for the rabbit population to double in size?

Answer 1

Explanation:

`p(t) = 50*2^(t)/(80)`

Let, the population of rabbits be p1 at day t1, and it will become double i.e. 2*p1 at day t2.

Total no. of days for doubling of population will be: (t2 - t1)

Now, for day t1:

`p_(1) =50*2^(t_(1) )/(80)`

For day t2:

`2*p_(1) =50*2^(t_(2) )/(80)`

Divide equation 2 by equation 1:

`2^1 = 2^(t_(2) - t_(1))/(80)`

Comparing the exponents of LHS and RHS:

`1 = (t_(2)-t_(1) )/(80)`

Hence, t2 - t1 = 80

Time for doubling will be 80 days

Answer 2

80 days

Explanation:

The equation ...

p(t) = 50(2)^(t/80)

tells you the value of p(t) will double when t increases by 80.

The population will double in 80 days.

_____

The order of operations requires that the equation in your problem statement be interpreted as ...

p(t) = 50(2^t)/80 = (5/8)2^t

This has a doubling time of 1 day, and starts with fractional rabbits.

Many curriculum materials suffer from poor editing of exponential equations. Any exponent that contains arithmetic operations must be enclosed in parentheses when it is written as plain text.