The number of computers sold by BCC depends on the dollar amount, x, that they spend on advertising. How many computers will they sell by spending $80,000 on advertising? Round to the nearest whole number and do not include units in your answer.
N(x) = 100 + 20 * In(0.25x)
N = 100 + 20 ln (20,000)
= 100 + 198
= 298
To find out the number of computers BCC will sell by spending $80,000 on advertising, we need to substitute x = $80,000 into the given equation N(x) = 100 + 20 * In(0.25x) and solve for N(x).
Here's how you can do it step by step:
Step 1: Substitute x = $80,000 into the equation:
N($80,000) = 100 + 20 * In(0.25 * $80,000)
Step 2: Simplify the expression inside the logarithm:
N($80,000) = 100 + 20 * In(0.25 * $80,000)
N($80,000) = 100 + 20 * In($20,000)
Step 3: Evaluate the natural logarithm:
Use a calculator or software that can calculate logarithms, and find the value of In($20,000). The natural logarithm of $20,000 is approximately 9.903487555.
N($80,000) = 100 + 20 * 9.903487555
Step 4: Perform the multiplication and addition:
N($80,000) ≈ 100 + 198.0697511
Step 5: Round the answer to the nearest whole number:
N($80,000) ≈ 298
Therefore, BCC will sell approximately 298 computers by spending $80,000 on advertising.