Jenny studied the characteristics of two species of bacteria. the number of bacteria of species a, a(t), after t hours is represented by the function, a(t) = 5 + (0.25t)3. the number of bacteria of species b, b(t), after t hours is represented by the function, b(t) = 2 + 8(1.06)t.

which function describes the difference in the number of bacteria, n(t), of both the species after t hours?

a.

n(t) = 3 + (0.25t)3 + 8(1.06)t

b.

n(t) = 7 + (0.25t)3 + 8(1.06)t

c.

n(t) = 7 + (0.25t)3 - 8(1.06)t

d.

n(t) = 3 + (0.25t)3 - 8(1.06)t

D .

Step-by-step explanation:

Given : Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is represented by the function,

The number of bacteria of species B, B(t), after t hours is represented by the function,

Then, the difference in the number of bacteria, N(t), of both the species after t hours will be :-

Hence, the correct answer should be : D .

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)