Mathematics, 18.07.2019 15:00 Olavarriafamily1

Timothy deposited $1,023.48 in a saving account that earns 2.4% simple interest. what will timothy’s account balance be in 5 months?

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Hello! The formula for simple interest is prt, meaning that you multiply the principal (initial amount) by the rate (simple interest rate) by the amount of time (could be in months or years). We have the principal and the annual simple interest rate, but we're talking 5 months time. There are 12 months in a year and 5/12 is equivalent to 0.416667 in decimal form. Let's solve it. 1,023.48 * 2.4% (0.024) is 24.56352 or 24.56 when rounded to the nearest hundredth. That's $24.56 in interest earned in 1 year. Now, let's multiply by by 0.416667 to get the amount of interest. 24.56 * 0.416667 is 10.23334152 or 10.23 when rounded to the nearest hundredth. $10.23 in interest is earned in 5 months. Now, let's add it into the initial amount. 1,023.48 + 10.23 is 1,033.71. There. Timothy's account balance will be $1,033.71 in 5 months.

Answer from: Quest

part a

answer: a reasonable domain is $0 \le n \le 10$ where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

=====================================

part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).

Answer from: Quest

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step-by-step explanation:

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Timothy deposited $1,023.48 in a saving account that earns 2.4% simple interest. what will timothy’s...