Question

Create your own real-world problem which uses either an arithmetic or geometric sequence to solve it. Include the solution, with work and explanation, to your problem.

Answer 1

The amount of bacteria in a researcher's dish increases at a rate of adding 4,000 to the previous amount every second. The starting amount of bacteria is 500,000, how many bacteria will there be in 5 seconds?

Explanation:

The amount of bacteria in a researcher's dish increases at a rate of 4,000 more than the previous amount every second. The starting amount of bacteria is 500,000, how many bacteria will there be in 5 seconds?

a(n) = 500,000 + 4,000 x n - 1

a(n) = 500,000 + 4,000 x 4

a(n) = 500,000 + 16,000

a(n) = 516,000 bacteria in 5 seconds

seconds bacteria

1 500,000

2 504,000

3 508,000

4 512,000

5 516,000

As you can see, both lead to the correct answer, which shows us we set up the formula correctly.

I'm always happy to help :)

Answer 2

Let's say that you're in your room and you find that the current temperature of 72 degrees is too cold, so slowly you increase the temperature of the room by two degrees.

We know that the explicit formula is
a^n=a^1+ (n-1)d

and so by substituting the given information in

a^n= 72 + (n-1)2

a^1=Initial temp
d= rate of change

by substitution a value of n (the term we are looking for) into this equation, you can then calculate the temperature that you just set the room too.