Years ago, The Insectarium decided to keep its population of 1420 Hercules beetles in an off-site facility. Over time, the population of Hercules beetles has increased by $5 \%$ annually.
Now 7 years later, the Hercules beetles will be moved to the new exhibit and kept in multiple glass enclosures.
Each glass enclosure costs $\$ 1800$ and can hold a maximum of 400 Hercules beetles.
The Insectarium will purchase the minimum number of glass enclosures needed to hold the Hercules beetles.
Answer
Calculate the total cost of the glass enclosures: \(5 \times 1800 = \boxed{9000}\)
Step 1 ：Calculate the current population of Hercules beetles after 7 years: \(1420(1 + 0.05)^7 \approx 1998.08\)
Step 2 ：Find the minimum number of glass enclosures needed: \(\lceil\frac{1998.08}{400}\rceil = 5\)
Step 3 ：Calculate the total cost of the glass enclosures: \(5 \times 1800 = \boxed{9000}\)
