An advertising agency conducted a survey and found that the number of units sold, N, is related to the amount 'a' spent on advertising (in dollars) by the following formula:
N= 1,500 + 400 ln a ( a ¡Ý 1 )
How many units are sold after spending $ 1,000 (to the nearest hole number)
To determine the number of units sold after spending $1,000 on advertising, we can substitute the value of a = 1,000 into the given formula and calculate N.
The formula given is:
N = 1,500 + 400 ln(a) (a ≥ 1)
Substituting a = 1,000 into the formula:
N = 1,500 + 400 ln(1,000)
Now, we need to calculate the natural logarithm of 1,000, denoted as ln(1,000). The natural logarithm (ln) is the logarithm with base e (approximately equal to 2.71828).
Using a scientific calculator, we find that ln(1,000) is approximately 6.9078.
Substituting this value into the formula:
N = 1,500 + 400 * 6.9078
Calculating:
N = 1,500 + 2,763.12
N = 4,263.12
Rounded to the nearest whole number:
N ≈ 4,263
Therefore, approximately 4,263 units will be sold after spending $1,000 on advertising.