Skills · Functions · Exponential Functions

Writing an exponential model

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

• grows by a percent: a town of 2,000 people grows 3% a year
• loses a percent: a $18,000 car loses 15% of its value each year
• doubles: a bacteria count of 50 doubles every hour
• halves: a 640-gram sample loses half its mass every year

Sample Sheet · Level 1

1. A town of 4,400 people grows 4% a year. Write y, the population after t years.
2. A $12,000 truck loses 20% of its value each year. Write y, its value after t years.
3. A $19,000 truck loses 10% of its value each year. Write y, its value after t years.
4. A town of 6,700 people grows 2% a year. Write y, the population after t years.
5. A $8,500 car loses 30% of its value each year. Write y, its value after t years.
6. A rabbit population of 500 grows 15% a year. Write y, the population after t years.
7. A rabbit population of 1,800 grows 10% a year. Write y, the population after t years.
8. A herd of 5,600 deer shrinks 5% a year. Write y, the herd after t years.

Answer key

1. y = 4,400(1.04)^t
2. y = 12,000(0.8)^t
3. y = 19,000(0.9)^t
4. y = 6,700(1.02)^t
5. y = 8,500(0.7)^t
6. y = 500(1.15)^t
7. y = 1,800(1.1)^t
8. y = 5,600(0.95)^t

Sample Sheet · Level 3

1. A savings account starts at $1,300 and earns 5% a year. Write y, the balance after t years.
2. A dish of 185 cells doubles every day. Write y, the count after t days.
3. A 300 mg dose of medicine halves every hour. Write y, the mg left after t hours.
4. A savings account starts at $6,900 and earns 2% a year. Write y, the balance after t years.
5. A $27,500 truck loses 10% of its value each year. Write y, its value after t years.
6. A herd of 6,800 deer shrinks 5% a year. Write y, the herd after t years.
7. A 580-gram sample loses half its mass every year. Write y, the grams left after t years.
8. A bacteria count of 135 doubles every hour. Write y, the count after t hours.

Answer key

1. y = 1,300(1.05)^t
2. y = 185(2)^t
3. y = 300(0.5)^t
4. y = 6,900(1.02)^t
5. y = 27,500(0.9)^t
6. y = 6,800(0.95)^t
7. y = 580(0.5)^t
8. y = 135(2)^t

Make your own

Pick the count, the level and the version, and print it with work space and the key on its own page. The same skill also makes an I Do, We Do, You Do lesson, a Mosaic, a Decoder and more.

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