Question

Money McGuire invests $50.00 in an account that she expects to double each year. How long will it take her investment to reach $3,200.00?

Answer 1

Money McGuire's investment will take 8 years to reach $3,200.00. This is because each year her investment will double, so her investment will double 8 times to reach $3,200.00. The equation for this is 2^8 x 50 = 3200.

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Answer 2

6 years

Explanation:

You want the length of time it takes for a $50 investment to total $3200 if it doubles in value each year.

Exponential equation

The value of the investment can be described by ...

v = 50·2^t

where t is the number of years.

You want t when v=3200:

3200 = 50·2^t

64 = 2^t

log(64) = t·log(2) . . . . . take logarithms

t = log(64)/log(2) = 6

It will take 6 years for her investment to reach $3200.

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Additional comment

If you're familiar with powers of 2, you recognize that 64 = 2⁶. Comparing exponents in ...

64 = 2^t

2^6 = 2^t . . . . . use 2^6 for 64

we can see that t=6. The logarithms are used to formalize this comparison.