Question

On the day Alexander was born, his father invested $5000in an account with a 1.2% annual growth rate. Write a function, A(t) that represents the value of this investment t year after Alexander's birth. Determine, to the nearest dollar, how much more the investment will be worth when Alexander turns 32 that when he turns 17.
A(t)=Answer
The investment will be worth$ Answer more when alexander turns 32 than when he turns 17

Answer 1

Answer:

Equation:  $A(t)=5000(1.012)^n$

Worth more in 32 yr than in 17 yr by:  $1199.92

Step-by-step explanation:

THe compound growth formula is:

$F=P(1+r)^n$

Where

F is the future amount (here, A(t))

P is the initial amount, here 5000

r is the rate of growth in decimal, 1.2% = 1.2/100 = 0.012

n is the time in years

Thus, we can say the function would be:

$A(t)=5000(1+0.012)^n\\A(t)=5000(1.012)^n$

Now, we want how much more it will be worth when 17 years and 32 years. We find the future amount, A(t), when n= 17 and n = 32 and find the difference. Shown below:

$A(t)=5000(1.012)^n\\A(17)=5000(1.012)^{17}\\=6124.05$

and

$A(32)=5000(1.012)^{32}\\=7323.97$

So, it will be worth more by:

7323.97 - 6124.05 = $1199.92