Sue set up a lemonade stand and sold 10 glasses of lemonade in the first hour. her sales increased at the rate of 20% per hour for the next n hours. which function represents the total number of glasses she sold in the nth hour? if the price of 1 glass of lemonade is $0.50, how much money did she earn in the nth hour? the function that gives the total number of glasses sold in the nth hour is , and the money she earned in the nth hour is .

This is compound interest

A=P(r+1)^t

r=rate

P=original amount

t=time in hours

A=10(.2+1)^t

A=10(1.2)^n is the number of glasses in n hours

price=cost time number of glasses

0.5 times is A=10(1.2)^n is 5(1.2)^n

total glasses sold in n hours is

f(n)=10 (1.2)^n

the function for money eraned in the nth hour is

f(n)= 5(1.2)^n

hope this helps

The appropriate exponential function for the first question is

... A: f(n) = 10 × 1.2^n

To find the revenue from sales of that many glasses, we multiply by the sale price to get

... B: 0.5(10 × 1.2^n)

This is compound interest

[tex]A=P(r+1)^t[/tex]

r=rate

P=original amount

t=time in hours

[tex]A=10(0.2+1)^t[/tex]

[tex]A=10(1.2)^n[/tex] is the number of glasses in n hours

price=cost time number of glasses

0.5 times [tex]10(1.2)^n[/tex] is [tex]5(1.2)^n[/tex]

total glasses sold in n hours is

[tex]f(n)=10(1.2)^n[/tex]

the function for money eraned in the nth hour is

[tex]f(n)=5(1.2)^n[/tex]

The 20% increase will be 2 more glasses of lemonade. So therefore now being 12 glasses of lemonade will be multiplied by 9hrs with result of 108 glasses- this will be the total number of glasses sold

If one glass costs $0.50 then the total costs will be

108 glasses × $0.50

answering=$54.00