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 = 3,500 + 200 ln a (a ≥ 1)
How many units are sold after spending $1,000? (Round your answer to the nearest whole number.)
well, what is
3500 + 200 ln(1000)
??
To find out how many units are sold after spending $1,000 on advertising, we can substitute the value of a = $1,000 into the given formula N = 3,500 + 200 ln a.
First, let's substitute a = $1,000 into the formula:
N = 3,500 + 200 ln (1,000)
Next, calculate the natural logarithm (ln) of 1,000:
ln (1,000) ≈ 6.907755
Now, substitute this value into the formula:
N = 3,500 + 200 * 6.907755
Multiply 200 by 6.907755:
N = 3,500 + 1,381.551
Add 3,500 and 1,381.551:
N ≈ 4,881.551
Finally, round the result to the nearest whole number:
N ≈ 4,882
Therefore, after spending $1,000 on advertising, approximately 4,882 units are sold.