The amount of a radioactive material changes with time. the table below shows the amount of radioactive material f(t) left after time t: t(hours) 0 1 2 f(t) 180 90 45 which exponential function best represents the relationship between f(t) and t?

Step-by-step explanation:

The general exponential function is written as :-

,where y is the amount of the material after t years , A is the initial amount and b is the multiplicative rate of growth or decay.

From the given table , f(0)=180

Thus the  initial value of radioactive material  =180

Also, the decay factor is the ratio of the consecutive terms :

Now, put A = 180 and b =0.5 in (i), we get

Therefore, the exponential function best represents the relationship between f(t) and t is

here

step-by-step explanation:

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you