A blood sample has 50,000 bacteria present. a drug fights the bacteria such that every hour the number of bacteria remaining, r(n), decreases by half. If r(n) is an exponential function of the number, n, of hours since the drug was taken, find the bacteria present four hours after administering the drug.

3125 bacteria

Step-by-step explanation:

Let r(0) be the initial amount of bacteria. Every hour, r(n) decreases by half. So, after one our new value for r(n) = (1/2)r(0). After two hours, r(n') =  (1/2)r(n) =  (1/2)(1/2)r(0) = (1/2)²r(0).

After n hours, r(n) = (1/2)ⁿr(0)

So when n = 4 hours and r(0) = 50,000, then

r(4) = (1/2)⁴r(0)

r(4) = (1/2)⁴ × 50,000

r(4) = (1/16) × 50,000

r(4) = 3125

So, after 4 hours, we have 3125 bacteria present.

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

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,