A quantity with an initial value of 450 grows exponentially at a rate of 0.4% every 10 years. What is the value of the quantity after 96 years, to the nearest hundredth?

467.58

Step-by-step explanation:

Grows 0.4% --> r = .004

Grows every 10 years: exponent of t/10

where t is in years

Write a function:

f(t) = 450(1+0.004)^t/10

96 years means no time conversion is needed due to years being the only unit in the problem

T = 96

f(96) = 450(1+0.004)^96/10

= 467.580247756

≈467.58

youre welcome y'all

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}