(t_n = ar^n-1) Sum of (n) terms: (S_n = \fraca(r^n-1)r-1, r\neq 1)
Key: (b>0, b\neq 1) If (b>1) → growth; if (0<b<1) → decay. functions grade 11 textbook
| Parameter | Effect | |-----------|--------| | (a) | vertical stretch ((|a|>1)) or compression ((0<|a|<1)), reflection in x‑axis if (a<0) | | (k) | horizontal stretch/compression, reflection in y‑axis if (k<0) | | (d) | horizontal shift (right if (d>0)) | | (c) | vertical shift (up if (c>0)) | (t_n = ar^n-1) Sum of (n) terms: (S_n
Find population after 10 hours: (P(10)=500\cdot 2^10/4=500\cdot 2^2.5=500\cdot 2^2\cdot 2^0.5=500\cdot 4\cdot \sqrt2\approx 500\cdot 5.657 = 2828) Inverse of exponential: (y = \log_b x \iff b^y = x) Domain: (x>0) Range: all real numbers However, I put together a structured “paper” /
A population starts at 500, doubles every 4 hours. Model: (P(t) = 500 \cdot 2^t/4) where (t) in hours.
However, I put together a structured “paper” / study guide that mirrors the key topics, learning objectives, and practice problems you would find in a typical Grade 11 Functions textbook (Ontario curriculum MCR3U).