Question

You decide to raise gerbils. Starting with three, you have nine at the end of 6 weeks, twenty-seven at the end of 12 weeks, and so on. The gerbil population triples every 6 weeks. How many gerbils will you have at the end of 24 weeks? Is the gerbil population growing arithmetically or geometrically? Note that the gerbil litters range from 2 to 5 and the gestation period is only about 31/2 weeks.

Answer 1

You will have 243 gerbils at the end of 24 weeks. The population grows geometrically, not arithmetically, tripling every 6 weeks.

Step-by-step explanation:

If you have gerbils that triple in quantity every 6 weeks, starting with 3 and having 9 at the end of 6 weeks, then the population growth can be modeled by the function G(t) = 3 × 3^t, where t is the number of six-week periods that have passed. To find the number of gerbils at the end of 24 weeks, we calculate G(4), because 24 weeks is four six-week periods:

• G(4) = 3 × 3^4
• G(4) = 3 × 81
• G(4) = 243 gerbils

Therefore, you will have 243 gerbils at the end of 24 weeks. This type of growth pattern is not arithmetic, where you would add the same number of gerbils each period; instead, it is geometric growth, where you multiply the population by a constant factor (in this case, three) every growth period.