Question

Scarlett bought an ant farm with 80 ants. Frond the following week forward, the ant population tripled every week. Let g(n) be the number on ants in scarletts farm in the nth week since she got it. G is a sequence. What kind is it? Write an explicit formula for the sequence starting with g(n)=? Need help really bad I’m stuck and can’t figure out what it is

Answer 1

Answer:

g(n)=80×3^(n-1)

Step-by-step explanation:

First term (a)=80

The ant population tripled every week.

So, the population of ant after 1st week will be (80 × 3) = 240

After 2 weeks, the population triples again.

We have, (240 × 3) = 720

Common ratio (r)=720/240

=3

r=3

The ants population is increasing in a geometric progression

A geometric progression is given by

g(n)=a × r^(n-1)

Substitute values of a and r to get the explicit formula

g(n)=a × r^(n-1)

g(n)=80×3^(n-1)