Element X is a radioactive isotope such that every 9 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 70 grams, how long would it be until the mass of the sample reached 56 grams, to the nearest tenth of a year?

2.9 years

Step-by-step explanation:

Given that :

Half-life t1/2 = 9 years

Initial mass = I = 70 grams

A = final mass = 56 grams

t = time taken to reach final amount

Using the exponential half life relation :

A = I(0.5)^t/t1/2

56 = 70(0.5)^t/9

56/70 = 0.5^t/9

0.8 = 0.5^t/9

Log 0.8 = log 0.5^t/9

−0.096910 = −0.301029 * t/9

t/9 = 0.096910 / 0.301029

t/9 = 0.3219291

t = 0.3219291 * 9

t = 2.8973619

t = 2.9 years

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.