Question

An investment made in the stock market decreased at a rate of 2.2% per year for 10 years. What is the current value of

Answer 1

Answer:

$800,500 (nearest dollar)

Step-by-step explanation:

The given scenario can be modeled as an exponential equation.

General form of an exponential function:

 $f(x)=ab^x$

where:

• a is the initial value (y-intercept)
• b is the base (growth/decay factor) in decimal form
• x is the independent variable
• y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

The initial value (a) is the value of the investment.

Therefore, a = 1,000,000.

If the investment decreases by 2.2% each year, then it will be 97.8% of the previous year.

Therefore, b = 97.8% = 0.978.

Substitute these values into the formula to create a general equation for the scenario:

$f(x)=1000000(0.978)^x$

(where x is the time, in years).

To find the value of the investment after 10 years, substitute x = 10 into the formula:

$\implies f(10)=1000000(0.978)^{10}=800500.1586$

Therefore, the value of the investment after 10 years is $800,500 (nearest dollar).

Learn more about exponential functions here:

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