Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.
Required skills (click to reveal)
A small town in regional Victoria has a population that grows exponentially according to the model P(t) = 8000 × e^(0.03t), where P(t) is the population after t years. After 10 years, what is the exact population of the town?
Express your answer as an exact exponential expression in the form 8000 × e^k, where k is a simplified exact number.
Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.
My notes — optional, not graded
0 wordsNotes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.
For this question only. Your full notebook is on the dashboard.
Notes save in this browser. Download a copy to keep them elsewhere.
Report a problem or suggest an improvement
Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.
Formula and explanation (click to reveal)
Opening this before your first submission makes the attempt practice only.
Formula
Explanation
Worked solution and answer (click to reveal)
Opening this before your first submission makes the attempt practice only.
Worked solution
- The population model is given as P(t) = 8000 × e^(0.03t), where t is time in years and P(t) is the population at time t.
- We are asked to find the population after 10 years, so substitute t = 10 into the model.
- P(10) = 8000 × e^(0.03 × 10)
- Calculate the exponent: 0.03 × 10 = 0.3
- Substitute the exponent back: P(10) = 8000 × e^0.3
- The expression 8000 × e^0.3 is already in the required form: 8000 × e^k, where k = 0.3.
- 0.3 is a simplified exact number (as a decimal fraction, 3/10), and no further simplification is needed.
- The final answer must be expressed as an exact exponential expression, not a decimal approximation.
- No rounding or approximation is required; the question asks for an exact expression.
- The value of k is 0.3, which is exact and simplified.
- The population after 10 years is exactly 8000 × e^0.3.
- This matches the required form and is the exact answer.
Reference answer: 8000 × e^0.3
Alternative methods (click to reveal)
Shortcuts are shown only when applicable. Check the conditions before using one.
Quick-method explanations are blurred in this trial preview. The standard formula and worked solution remain available.
Earlier attempts for this question
| # | Date / time | Your answer | Result | Seconds | Help revealed | Rank |
|---|
Worksheet details
Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html
Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.
NavGanitMate privacy & saved work
Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.
Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.
Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.
A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.
Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.
Files ready to save
If a file opens instead of downloading, use its save link below or your browser’s Save As command.