# How do you determine if the equation y= 0.5 (0.9)^x represents exponential growth or decay?

Anything to the $x$ will be growth, if it's ${n}^{\textcolor{red}{-} x}$ then it'll be decay.
${n}^{- x} = \frac{1}{n} ^ x$
Therefore as $x$ increases, $y$ will decrease.
When you have ${n}^{x}$ as $x$ increases so will $y$.
{"ft_lang_label":"__label__en","ft_lang_prob":0.59221935,"math_prob":0.99999595,"size":299,"snap":"2023-14-2023-23","text_gpt3_token_len":76,"char_repetition_ratio":0.108474575,"word_repetition_ratio":0.0,"special_character_ratio":0.24749164,"punctuation_ratio":0.0877193,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9999976,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-03-27T16:55:49Z\",\"WARC-Record-ID\":\"<urn:uuid:79c57c79-ef34-45c2-9287-6a272d6204e6>\",\"Content-Length\":\"32672\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:dfb1fc25-f2ef-4646-b11a-feaad6f68a6c>\",\"WARC-Concurrent-To\":\"<urn:uuid:3b80cbf7-9471-4f65-90b2-be9ce98f5bd8>\",\"WARC-IP-Address\":\"216.239.34.21\",\"WARC-Target-URI\":\"https://socratic.org/questions/how-do-you-determine-if-the-equation-y-0-5-0-9-x-represents-exponential-growth-o\",\"WARC-Payload-Digest\":\"sha1:SSWXPMCAQSFS7WEBH5YTELZMR2T6WNAK\",\"WARC-Block-Digest\":\"sha1:WYAW33CFSXAIZ57LITN5MCZDN5M347FX\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-14/CC-MAIN-2023-14_segments_1679296948673.1_warc_CC-MAIN-20230327154814-20230327184814-00341.warc.gz\"}"}