Answer:
300
Step-by-step explanation:
im smart
Answer:
S'(x)=-0.006x2+0.8x+9
Step-by-step explanation:
The rate of change of the sales S(x) with respect to the amount of money spent on advertising x is then the derivative of S(x) with respect to x. What we have to calculate is S'(x).
We know that the derivative of 
is 
(where a is a constant), and the derivative of a sum is the sum of the derivatives, so we can calculate the derivative of each term independently:
S'(x)=(−0.002x3 + 0.4x2 + 9x + 500)'=(−0.002)(3)x2 + (0.4)(2)x + 9
Which means:
S'(x)=-0.006x2+0.8x+9
Answer:
120.085366
Step-by-step explanation:
Answer:
745 books are expected to be donated to the library at the end of Month 10
Step-by-step explanation:
There were 80 books donated at the library:
No=80
The number of books donated to a library is increasing by 25% each month:
There were 100 books donatd at the end of Month 1:
N1=100
N1=No+25%No
N1=No+(25/100)No
N1=No+0.25 No
N1=(1+0.25) No
N1=(1.25) No
(1) N1=(1.25)^1 No
N1=(1.25)^1 80
N1=(1.25) 80
N1=100
N2=N1+25%N1
N2=N1+(25/100)N1
N2=N1+0.25 N1
N2=(1+0.25) N1
N2=(1.25) N1
Replacing equation (1) in the equation above:
N2=(1.25) (1.25)^1 No
N2=(1.25)^(1+1) No
(2) N2=(1.25)^2 No
N3=N2+25%N2
N3=N2+(25/100)N2
N3=N2+0.25 N2
N3=(1+0.25) N2
N3=(1.25) N2
Replacing equation (2) in the equation above:
N3=(1.25) (1.25)^2 No
N3=(1.25)^(1+2) No
(3) N3=(1.25)^3 No
In general:
Nt=N(t)=(1.25)^t No
N(t)=(1.25)^t (80)
N(t)=80 (1.25)^t
where t is the number of the month
How many books are expected to be donated to the library at the end of Month 10?
t=10
N(10)=80 (1.25)^10
N(10)=80 (9.313225746)
N(10)=745.0580596
Rounding to the nearest whole number:
N(10)=745
