The chemical element einsteinium-
253
253253 naturally loses its mass over time.
The relationship between the elapsed time
t
tt, in weeks, since a sample of einsteinium was measured, and its mass,
M
(
t
)
M(t)M, left parenthesis, t, right parenthesis, in grams, is modeled by the following function:
M(t)=(0.97)7t+5
Every week, the mass of the sample is multiplied by a factor of

Every week, the mass of the sample is multiplied by a factor of 0.81

Step-by-step explanation:

Let's rewrite the base and find the expression whose exponent is just ttt.

(0.97)7t+5=(0.97)7t⋅(0.97)5=(0.977)t⋅(0.97)5

Therefore, we can rewrite the modeling function as follows.

M(t)=(0.97)5⋅(0.977)t

According to this model, the mass of the sample is multiplied by 0.977 every week. Rounding this to two decimal places, we get 0.977≈0.81.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)