Question

Need Help Please with q2 & q4!!

Question 2: ARITHMETIC SEQUENCES AND SERIES
Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase under her bed, modeled by the function s(x) = 450. She is able to babysit to earn extra money and that function would be a(x) = 6(x − 2), where x is measured in hours. Explain to Tamara how she can create a function that combines the two and describe any simplification that can be done.

Question 4: GEOMETRIC SEQUENCES
Tommy has $350 of his graduation gift money saved at home, and the amount is modeled by the function h(x) = 350. He reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.04)^x−1. Explain how Tommy can combine the two functions to model the total amount of money he will have in his bank account as interest accrues after he deposits his $350. Justify your reasoning.

Answer 1

Question 2: The first function represents the amount of money she'll have from her 450 under her bed.

s(x) = 450

The second function represents the amount of money she'll earn from babysitting per hour (x):

a(x) = 6(x - 2)

To figure the combined amount, we can add the two functions:

f(x) = s(x) + a(x)

f(x) = 450 + 6(x - 2)

From there, she can simplify the function by distributing, then combining the like terms to simplify:

f(x) = 450 + 6x - 12

f(x) = 438 + 6x

Answer:

f(x) = 438 + 6x

Question 4: His functions are;

h(x)=$350

s(x)=(1.04)^x-1

To find total amount of money in Tommy's account using the functions above, we substitute the first equation x=$350 in the second function.