Question

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

Answer 1

.81

Explanation:

I got it right on Khan Academy.

Answer 2

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

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.