- After [latex]7[/latex] years, Marko will have planted a total of [latex]55[/latex] tulips in his yard. To have planted at least [latex]113[/latex] tulips, it will take Marko approximately [latex]18.6[/latex] years.
- In [latex]12[/latex] years, Pam will have a total of [latex]2,322[/latex] albums in her collection. To reach at least [latex]500[/latex] albums, it will take Pam approximately [latex]0.32[/latex] years.
- In the year 2030, the store’s annual sales will be $190,000. The store’s sales exceeded [latex]$100,000[/latex] in the year 2024.
- In the year 2007, there would be [latex]500[/latex] houses in the town. The number of houses would have reached at least [latex]400[/latex] by the year 2003.67. Given that we measure time in whole years, we would round this to the nearest whole number. Since reaching [latex]400[/latex] houses occurs partway through the year, the town would have crossed the threshold in 2004.
- The linear equation in slope-intercept form that predicts the number of beetles in the population in week [latex]n[/latex] is: [latex]y=8n+3[/latex], where [latex]y[/latex] is the number of beetles and [latex]n[/latex] is the number of weeks.
- The linear equation in slope-intercept form that predicts the number of streetlights in the town in month [latex]n[/latex] is: [latex]y=4n+130[/latex], where [latex]y[/latex] is the number of streetlights and [latex]n[/latex] is the number of months since the initial count.
- In the year 2016, the population of Tacoma would be approximately [latex]794,061[/latex]. The population would exceed [latex]400,000[/latex] around the year 2008.04. Given that we measure time in whole years, we can conclude that the population of Tacoma exceeded [latex]400,000[/latex] in the year 2008.
- In the year 2016, Portland’s population would be approximately [latex]626,771[/latex]. Portland’s population will reach [latex]700,000[/latex] around the year 2026.10. Given that we measure time in whole years, it can be concluded that the population of Portland is expected to reach [latex]700,000[/latex]in the year 2026.
- Under the exponential growth model with a [latex]2\%[/latex] annual growth rate, the projected world population in 2015 would be approximately [latex]8.71[/latex] billion. The world population would have reached [latex]10[/latex] billion around the year 2022.
- After correcting the calculation, the projected number of bacteria in [latex]1[/latex] day ([latex]24[/latex] hours) is approximately [latex]6,430[/latex] bacteria.
- The projected wolf population will be about [latex]544[/latex] wolves in [latex]10[/latex] years.
- Two years after the trout were seeded into the lake, the population is projected to be approximately [latex]352[/latex] trout. It would take a little over [latex]4[/latex] years for the trout population in the lake to grow to [latex]1,000[/latex].
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- After [latex]1[/latex] month: [latex]32[/latex] plants
- After [latex]2[/latex] months: [latex]47[/latex] plants
- After [latex]3[/latex] months: [latex]50[/latex] plants (rounded to the nearest whole number)
- After [latex]4[/latex] months: [latex]50[/latex] plants
- After [latex]5[/latex] months: [latex]50[/latex] plants
What appears to be happening to the number of plants in the yard over time is that the population initially grows rapidly due to the high growth rate of [latex]200\%[/latex] per month. However, as the population approaches the yard’s carrying capacity of [latex]50[/latex] plants, the growth rate slows down, and the number of plants stabilizes near the carrying capacity.
- The model predicts that the minimum wage in 1960 would have been approximately [latex]$1.11[/latex]. According to the exponential growth model, the minimum wage in 1996 would have been approximately [latex]$5.70[/latex]. Comparing the model’s prediction to the actual minimum wage of [latex]$5.15[/latex] in 1996, we see that the model’s prediction is above the actual figure.