Question

Peter purchases a baseball card for $150 as an investment. His research tells him that the value of

Answer 1

Answer:

6 years

Step-by-step explanation:

Given

$Initial\ Investment = 150$

$Ratio = double$

Required

When will it get to 4000

This question illustrates a geometric progression and will be solved using:

$T_n = ar^{n-1}$

In this case;

$T_n = 4000$

$r = double = 2$

$a = 150$

So, we're to solve for n

$4000 = 150 * 2^{n - 1}$

Divide through by 150

$\frac{4000}{150} = 2^{n-1}$

$26.67= 2^{n-1}$

Take Log of both sides

$Log26.67= Log2^{n-1}$

Apply law of logarithm

$Log26.67= ({n-1})Log2$

Take Log values

$1.42602301569 = (n - 1) * 0.30102999566$

Make n - 1 the subject

$n - 1 = \frac{1.42602301569}{0.30102999566}$

$n - 1 = 4.73714591984$

Add 2 to both sides

$n = 1 + 4.73714591984$

$n = 5.73714591984$

$n = 6$ (Approximated)

Hence, it'll take 6 years