### Problem Statement**12.** Benny received 4 pennies on the first day of the month, and each day after that, he received quadruple the number of pennies that he received the day before. On what day of the month did Benny first receive over 1 million dollars on a single day?### ExplanationIn this problem, Benny's pennies grow exponentially, quadrupling each day. Here is the breakdown:- Day 1: 4 pennies- Day 2: 4 x 4 = 16 pennies- Day 3: 16 x 4 = 64 pennies- Day 4: 64 x 4 = 256 pennies- ...Let’s denote the number of pennies Benny receives on the $ n $th day as $ P(n) $. The relationship can be expressed mathematically as:\[ P(n) = 4 \times 4^{(n-1)} = 4^n \text{ pennies} \]To find out when Benny first receives over 1 million dollars, knowing that 1 dollar = 100 pennies, we set up the inequality:\[ 4^n > 100 \text{ (pennies needed for 1 dollar)} \times 1,000,000 \text{ (number of dollars)} \]\[ 4^n > 100,000,000 \]Taking the logarithm (base 10) of both sides, we get:\[ \log_{10}(4^n) > \log_{10}(100,000,000) \]\[ n \log_{10}(4) > 8 \]\[ n > \frac{8}{\log_{10}(4)} \]Using the value $ \log_{10}(4) \approx 0.602 $:\[ n > \frac{8}{0.602} \approx 13.29 \]Since $ n $ must be a whole number (representing days), Benny first receives over 1 million dollars on the 14th day of the month.### ConclusionBenny first receives over 1 million dollars on a single day on the 14th day of the month.

Given: Money received on Day 1 = 1 penny Money is being quadrupled every day. So, Money received on…

12. Benny received 4 pennies on the first day of the month, and each day after that, he received quadruple the number of pennies that he received the day before. On what day of the month did Benny first receive over 1 million dollars on a single day?

12. Benny received 4 pennies on the first day of the month, and each day after that, he received quadruple the number of pennies that he received the day before. On what day of the month did Benny first receive over 1 million dollars on a single day?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Similar questions

After a month of saving your allowance, you accumulated 10,000 in your account. You want to make more of this money and you just heard from your friends about “investing”. So you posted on your Facebook that you are looking for something you can invest your money. Two of your friends commented. One friend says, “Invest to me and after one month, your money will increase by 20% every 10 days.” Another friend of yours says, “Invest to me and your money will increase by 30% every 15 days for a month.” To whom you will invest?math
2. Franklin was smart and bought all of his textbooks for college used. This way, he saved 30% on the original price of the textbooks. If the books would have originally cost $315 dollars, how much did Franklin pay? After a 30% discount is removed, what percentage of the original cost remains? How much did Franklin pay?
Samsan Tech, had been mailing out coupons for sale of shares at a constant rate for 4 days, when they counted the coupons, they still had mail out and discover they had 120,000 left. After 7 total days of work they had 75,000 left. At what rate are they mailing coupons out? a. 17,000 coupons per day b. 15,000 coupons per day c. 11,000 coupons per day d. 13,000 coupons per day
2. Maria deposits $10,000 in the bank. Each month thereafter she deposits $1000 a month . Use formulas to determine how much money she will have in the bank after 2 years? (month 24) .
1. Jing 1/4 spent of her money on a pack of pens, 1/2 of her money on a pack of markers, and 1/8 of her money on a pack of pencils. What fraction of her money is left?
XYZ Corporation manufacturers bookcases that it sells for P65.00 each. It costs XYZ P35,000.00 per year to operate its plant. This sum includes rent, depreciation charges on equipment, and salary payments. If the cost to produce one bookcase is P50.00, how many cases must be sold each year for XYZ to avoid taking a loss?
VongVong lent 6,000 pesos to Lenni for 2 years and 1500 pesos to Hisko for 4 years and received altogether from both 900 pesos as Simple Interest. What is the rate of interest? * 7% 5% 4.5% 10% 800 pesos amounts to 920 pesos in 3 years at Simple Interest. If the interest rate is increased by 3%, what would it amount to? 992 1182 996 1026
Ernie wrote 10 checks last month and these were the only transactions for his checking account. According to his check register, his balance is $1884.88, but the bank statement he just received says his balance is $2117.29. If nine of Ernie's 10 checks have cleared, what is the amount of the check that hasn'tyet cleared?