Question

1. A population of lab rats is going to be increased by 3 rats a month. If it costs $3.50 to

care for each rat a month and there were 2 rats to begin with in the lab. (Assume all
rats survive lab work)
a. Create a formula that would represent the population of lab rats in month n.
b. How much will the lab be paying for the rats after 10 months?
C. After how many years will the lab rats population reach 326?​

Answer 1

a. p(n) = 3n -1

b. $101.50

c. 9 years

Explanation:

a. The number of rats in any given month is an arithmetic sequence with first term 2 and common difference 3:

for months 1, 2, 3, 4, the rat population is 2, 5, 8, 11.

The usual formula for the n-th term of an arithmetic sequence applies:

a[n] = a[1] +d(n -1)

a[n] = 2 +3(n -1) = 3n -1

In month n, the population of lab rats is ...

p(n) = 3n -1

__

b. After 10 months, the population will be ...

p(10) = 3·10 -1 = 29

At $3.50 per rat, the cost will be ...

29 · $3.50 = $101.50

__

c. We want to find for p(n) = 326.

326 = 3n -1

327 = 3n

109 = n

Month 109 is 108 months (9 years) after month 1. The population will reach 326 rats in 9 years.