Jackie’s grandfather gave her $250 for her birthday. To make her birthday money last, Jackie asked her mother to save it for her and only give her a $10 bill each Monday. The function A(t) = 250 – 10t can be used to represent the amount of money remaining each week as a function of the number of weeks elapsed since she gave the money to her mother to manage. What is the domain of the function for this situation?

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: