Use the table at the right to find the value of t(20).

Question

The table includes n values (x- value) of 1,2,3,4, and 5. The table doesn't have a t(n) (y value) value for 1 or 2, but 3's value is 24, 4's value is 48, and 5's value is 96. How do you find t(20)?

Answer 1

To start out, you want to look for a pattern. In this case, as x goes up, the y value is being multiplied by 2, making it exponential growth. This means our base equation is 2^x.

Now lets plug in our x values to find out what 2^x is multiplied by in the equation.

2^3 = 8, but t(3) is 24. This means 2^x could be multiplied by 3 to equal 24. Let's test this out with the other x values

2^4 = 16, 16*3 = 48, which is in fact, t(4)

2^5 = 32, 32*3 = 96, which is in fact, t(5)

This means our equation is 3*(2^x). We can now simply plug in 20 into this equation, which gives us 3145728 as the final answer.

Answer 2

You can figure out the relationship, come up with the equation and then use that equation to solve for t(20)

By the y values provided, the y values are doubling. That means an exponential equation with a b value of 2

y=a(b)^x

y=a(2)^x

To solve for a you could use 2 of the data points, and solve 2 equations 2 unknowns. Since you know they are doubling you could also work backward manually to get t(0). I got this equation using the second method.

y=3(2)^x

Now plug in 20

y=3(2)²⁰

3,145,728