Question

For how many (not necessarily positive) integer values of n is the value 4000x(0.4)^n an integer?

Answer 1

The number of integer values of n for which the value 4000 × (0.4)ⁿ is an integer is; 9

How to find the integer values in algebra?

We are given the expression;

4000 × (0.4)ⁿ

This can also be expressed as;

4000 × (²/₅)ⁿ which can further be expressed in exponent form as;

(2⁵ × 5³) × (²/₅)ⁿ = 2⁽⁵ ⁺ ⁿ⁾ × 5⁽³ ⁻ ⁿ⁾

Since this expression is an integer, we need:

1) 5 + n ≥ 0 for which n ≥ -5

2) 3 - n ≥ 0 for which n ≤ 3

Taking the intersection gives;

-5 ≤ n ≤ 3

Thus;

Number of Integer Values = 3 - (-5) + 1 = 9

Read more about Integer Values at; brainly.com/question/17695139

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