Answer: 336 beetles remain after 6 weeks.
Explanation:
If there are 1280 beetles in the city and every week 20% of them die, then the rate is exponential. The formula for determining the number of beetles left in the city after t weeks would be
A = P(1 - r/n)^nt
Where
A represents the number of beetles left after t years.
P represents the initial number of beetles
r represents the death rate of the beetles.
n represents the periodic record of the death.
t represents the number of weeks.
From the information given,
P = 1280
r = 20/100 = 0.2
n = 1(recorded weekly)
t = 6 weeks
Therefore,
A = 1280(1 - 0.2/1)^1 × 6
A = 1280(0.8)^6
A = 336