Exponential equation:
Initial monthly sales a = $1,480. Monthly increase = 1/7, so growth factor b = 1 + 1/7 = 8/7.
Therefore the model is:
y = 1480(8/7)x, where x is months after starting the ad campaign.
When will sales be greater than $2,000?
We solve 1480(8/7)x > 2000.
Divide both sides by 1480: (8/7)x > 2000/1480 = 50/37 ≈ 1.35135.
Take natural logs: x > ln(50/37) / ln(8/7) ≈ 0.301105 / 0.133532 ≈ 2.255.
So x must be greater than about 2.255 months. The number of whole months after the campaign when sales first exceed $2,000 is 3 months.
Quick check:
After 2 months: y ≈ 1480(8/7)2 ≈ $1,933.06 (still under $2,000).
After 3 months: y ≈ 1480(8/7)3 ≈ $2,207.81 (over $2,000).