Answer: At 17 months 17,275 ants will live in the colony
Number of months since the new colony was created: x
Number of ants: y
y=a(b)^x
At the beginning 38 ants, including the queen, created a new colony:
x=0→y=38:
38=a(b)^0
38=a(1)
38=a
a=38
y=38(b)^x
After 9 months there are now 970 ants:
x=9→y=970
970=38(b)^9
Solving for b. Dividing both sides by 38:
970/38=38(b)^9/38
25.52631578=b^9
ninth root:
ninth root (25.52631578)=ninth root (b^9)
1.433283216=b
b=1.433283216
y=38 (1.433283216)^x
At 17 months, how many ants will live in the colony?
x=17, y=?
y=38 (1.433283216)^17
y=38 (454.6155221)
y=17,275.38984
y=17,275