Answer:
a) growth
b) $500
c) 6% = 0.06
d) [tex]f(x)=500(1.06)^x[/tex]
e) $595.51
Step-by-step explanation:
Part (a)
Exponential GROWTH, since interest is applied to the account each year.
Part (b)
Initial amount = $500
Part (c)
Growth factor = 6% = 0.06 (in decimal form)
Part (d)
General form of exponential growth function:
[tex]f(x)=a(1+r)^x[/tex]
where:
- a = initial amount
- r = rate of growth (in decimal form)
- x = time (in years)
Given:
[tex]\implies f(x)=500(1+0.06)^x[/tex]
[tex]\implies f(x)=500(1.06)^x[/tex]
Part (e)
when x = 3
[tex]\begin{aligned}\implies f(3) & =500(1.06)^3\\ & = 595.51\: \sf(nearest\:hundredth)\end{aligned}[/tex]
