Question

An investment of $5000 in a bank account doubles every 4 years. The function that models the growth of this investment is f(x)=5000*2ˣ, where x is the number of doubling periods. How much will the investment be worth after 8 doubling periods?

Answer 1

The value of the $5000 investment after 8 doubling periods will be $1,280,000, by substituting the number of doubling periods (8) into the investment's growth function: f(x)=5000*2ˣ.

Step-by-step explanation:

The question pertains to the topic of exponential growth in the context of an investment of $5000 in a bank account, which doubles every 4 years. The function given that models this growth is f(x)=5000*2ˣ, where x is the number of doubling periods.

To find the value of the investment after 8 doubling periods, we substitute x=8 into the function, yielding f(8)=5000*2⁸. The result, calculated as f(8)=5000*256, is $1,280,000. This means after 8 doubling periods, the investment will be worth $1,280,000.

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