Intermediate algebra help

Question

The number of grams of radioactive cesium that remain after t years from an original sample of 30 g is given by N(t) = 30(2–0.0322t). Using a graphing calculator, graph N and determine in how may years there will be 20 g of cesium remaining.

Answer 1

I am going to work the problem assuming the correct formula is

N(t) = 30 e^-0.0322t

 

where N(t) is the mass in grams of Cesium remaining after t years, and N(0) = 30 g.

Let T = number of years that it takes for the Cesium mass to drop to 20 g.  Then

 

20 = 30 e^-0.0322T

 

T = ln(20 / 30) / (-0.0322) years = 12.592 years

Answer 2

Did you program function on your graphing calculator, as directed?  Its graph is a line.

If you also program another function, y = 20, that will be a horizontal line (graph of constant).

The point at which they intersect is what you want.  Use calculator to find the t value of that intersection.

 

It's also possible to solve algebraically:  solve 20 = 30(2–0.0322t)