The amount of polonium-210 remaining, p(t), after t days in a sample can be modeled by the exponential function p(t) = 100e−0.005t, where 100 represents the initial number of grams in the sample. what is an equivalent expression, written as a percentage rate of polonium-210 lost, and how much polonium-210 remains (rounded to the nearest whole number) after 63 days?

% Po lost = 100[1 - e^(-0.005t)]  %; 73.0 g

Step-by-step explanation:

p(t) = 100e^(-0.005t)

Initial amount:        p(0) = 100

Amount remaining: p(t) = 100e^(-0.005t)

Amount lost: p(0) – p(t) = 100 - 100e^(-0.005t) = 100[1 - e^(-0.005t)]

% of Po lost  = amount lost/initial amount × 100 %

= [1 - e^(-0.005t)]  × 100 % = 100[1 - e^(-0.005t)]  %

p(63) = 100e^(-0.005 × 63) = 100e^(-0.315) = 100 × 0.730 = 73 g

The mass of polonium remaining after 63 days is 73 g.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500