f(x) is an exponential growth function.Β It can be modeled asΒ
, where a is the initial amount, r is the interest rate in decimal form, andΒ t is the time period.Β When the values from the scenario are plugged in, it looks likeΒ
.Β On a graph,Β aΒ will be the y-intercept, so the y-intercept of f(x) is 6.
g(x)Β has a y-intercept that must be less than 6.Β The function reaches a y-value of 6 whenΒ xΒ = 1, not 0 (whenΒ x = 0,Β we are given the y-intercept).Β We see that as y decreases x decreases, so it is confirmed that g(x) has a y-intercept that is < 6.Β Already we know that its y-intercept is less than that of f(x).
h(x)Β visibly intercepts the y-axis at y = 4.Β Its y-intercept is 4.
j(x)Β is written in exponential growth format (like f(x)), where the initial amount,Β a, would be the y-intercept.Β 10 is its y-intercept.
After evaluating the y-intercepts of each of these functions, it is determined that j(x) has the highest y-intercept.