# Find the vertical & horizontal factors and horizontal translation of an exponential function when only given certain points (high school math).

I really need help solving this problem, and I hope I came to the right place (this is my first time on this site)! For a certain exponential function, I was given the points (-10, 1.9968), (-9,1.984), (-8, 1.92), (-7,1.6) and (-6,0). By the points, I was able to make some conclusions for the exponential function:

y = -a(5)^[k(x-d)] +2,

the b-value is 5, the c-value (or the asymptote) is 2, and the a-value is negative, as the function portrays to be decaying. I am in need of finding the a, k and d values of this exponential function, as I need it for a math assignment due soon. I would like to know if this is high school level math, as I may be interpreting the question differently. Thank you very much and I appreciate all your replies.

• least squares between log y and x – Narasimham Jan 19 '18 at 4:37

You have an extra parameter in your equation because $5^{-kd}$ can be absorbed into $a$, so now your equation is $y=-a5^{kx}+2$. If you subtract $2$ and take the log you get $\log_5(2-y)=\log_5(a)+kx$. This is a straight line in $x$ vs $\log_5(2-y)$ and you should be able to find $k$. I plotted the points and they look to fit a straight line nicely.
• Then $a$ and $d$ are equivalent just as I said. You can just set $d$ to zero and find the proper $a$. $d$ just makes a factor of $5^{-kd}$, and given $k=1$ this is $5^{-d}$. It is a multiplicative factor just like $a$, so the two of them are only one variable. If there is no noise in your data, you can just take one point and evaluate $a$. Otherwise you can compute $a$ from each point and take some sort of average. – Ross Millikan Jan 20 '18 at 3:41
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://math.stackexchange.com/questions/2611694/find-the-vertical-horizontal-factors-and-horizontal-translation-of-an-exponent", "fetch_time": 1568577540000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2019-39/segments/1568514572289.5/warc/CC-MAIN-20190915195146-20190915221146-00136.warc.gz", "warc_record_offset": 599906554, "warc_record_length": 31451, "token_count": 496, "char_count": 1773, "score": 4.1875, "int_score": 4, "crawl": "CC-MAIN-2019-39", "snapshot_type": "latest", "language": "en", "language_score": 0.9268026947975159, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00013-of-00064.parquet"}